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REVIEW ARTICLE
Subsonic jet aeroacoustics: associating experiment, modellingand simulation
Peter Jordan Æ Yves Gervais
Received: 18 December 2006 / Revised: 12 September 2007 / Accepted: 12 September 2007 / Published online: 17 October 2007
� Springer-Verlag 2007
Abstract An overview of jet noise research is presented
wherein the principal movements in the field are traced
since its beginnings. Particular attention is paid to the
evolution of our understanding of what we call a ‘‘source
mechanism’’ in free shear flows; to the theoretical, experi-
mental and numerical studies which have nurtured this
understanding; and to the currently unresolved conceptual
difficulties which render analysis of experimental and
numerical data so difficult. As it is clear that accelerated
progress in this field of research can be made possible by a
more effective synergy between the theoretical, experi-
mental and numerical disciplines—one which draws in
particular on the impressive recent progress in experi-
mental and numerical techniques—we endeavour to
elucidate the various ‘‘source’’ characteristics identified by
these different means of study; the points on which the
studies agree or disagree, and the significance of such
accord or discord; and, the new analysis possibilities which
can now be realised by effectively associating experiment,
modelling and simulation.
1 Introduction
The science of aeroacoustics is now over fifty years old,
and the considerable range of analysis strategies which
have evolved during this time have seen much progress.
Experimental diagnostics have become more sophisticated,
as a result of improvements in measurement technology,
and the more ambitious and innovative data extraction and
analysis techniques which these improvements have
encouraged. The numerical simulation constitutes a rela-
tively recent aid to our understanding of the most
fundamental aspects of the physics of sound production: as
this discipline matures more light is shed on the subtleties
which comprise the source mechanisms in jets, and guid-
ance is provided, both for jet-noise modelling strategies,
and for the implementation of perspicacious experimental
measurement and analysis. As a result of this enhanced
measurement and analysis capability, our understanding of
the mechanisms underlying the production of sound by un-
bounded turbulence has improved, old ideas have been
revisited, and new challenges identified.
In this paper we present an overview of this progress,
with an emphasis on the association of experiment, mod-
elling and simulation. The paper is organised as follows. In
Sect. 2 we endeavour to clearly identify where we cur-
rently stand in terms of our understanding of the sound
production mechanisms in jets, and to outline the road by
which we have arrived at this point. This overview is fol-
lowed in Sect. 3 by a review of the more pertinant
experimental studies which have appeared in recent years,
and as some of the more interesting results have been
produced as a result of progress in measurement technol-
ogy, we pay particular attention to the new measurement
strategies which this progress has made possible. We out-
line and discuss the novel analysis procedures which have
accompanied these, and the impact that the results have had
on the way we attempt to model aerodynamically generated
sound. In Sect. 4 we look briefly at contributions from
numerical aeroacoustics, in terms of the physical insights
which these have provided, and finally a resume of some
current ideas regarding the dominant source mechanisms in
jets is provided in Sect. 5.
P. Jordan (&) � Y. Gervais
Laboratoire d’Etudes Aerodynamiques, UMR CNRS 6609,
Universite de Poitiers, Poitiers Cedex, France
e-mail: [email protected]
123
Exp Fluids (2008) 44:1–21
DOI 10.1007/s00348-007-0395-y
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To close the paper we discuss the implications of the
most recent analysis strategies for future aeroacoustic
research, highlighting in particular the weak points, where
additional energy needs to be focused, but also indicating
the possible directions in which the stronger points can
now be steered in order to further untangle our under-
standing of the noise-producing jet.
2 Where do we currently stand, and how did we get
here?
In order to put recent developments in their proper context
we here provide a brief history of aeroacoustics with regard
to the unbounded turbulent jet. While such a summary
cannot hope to be exhaustive in such a small number of
pages, we hope nonetheless to provide a relatively com-
prehensive outline of the main movements in this field
since its beginnings in the early 1950s.
2.1 Early ideas of the sound-producing jet
To begin it is worth pointing out that in fact, contemporary
with Lighthill (1952), other researchers were also beginning
to touch on the theoretical aspects of aerodynamically
generated sound: Moyal (1952) for example, in a study
focused on the spectra of turbulence in compressible fluid
media, had demonstrated how spectral components of the
turbulent velocity field lying normal to the wavenumber
vector (turbulent eddies) would excite velocity, pressure
and temperature components lying parallel to the wave-
number vector (acoustic perturbations) by means of non-
linear inertia terms. However, there is no question that the
real birth of aeroacoustics as we know it today is due to
Lighthill, whose more specific focus on the problem of
aerodynamically generated sound led to the observation that
the exact equations of fluid motion can be recast in the form
of an inhomogeneous wave equation, whose inhomogeneity
comprises all the non-linearities of the Navier–Stokes
equations. Such an equation describes freely propagating
linear disturbances (an acoustic field) which are driven by
the dynamics described by a non-linear term on the right-
hand-side. Lighthill recognised that this form is particularly
well-suited to the problem of the noise-producing jet, as
such a flow system comprises precisely this: a freely prop-
agating sound field, which is driven by a confined region of
intense rotational motion, where non-linearity reigns.
As this kind of differential equation had been familiar to
scientists for some time, mathematical tools were readily
available for its manipulation, and so a solution was forth-
coming whence it was possible to establish a number of
facts, which subsequently came to constitute our first ideas
on the mechanisms underlying the production of sound by
turbulence. The jet was known to comprise random turbulent
fluctuations, correlated over a spatiotemporal extent defined
by the integral scales of the turbulence. The double spatial
derivative in Lighthill’s source term implied a quadrupole
behaviour, and so the sources of jet noise came to be
understood as quadrupole elemental deformations associ-
ated with these correlated turbulent eddies. The spatial
extent of the eddies was supposed considerably less than the
wavelength of the sound waves transmitted from the flow,
implying that the quadrupole ‘‘sources’’ are acoustically
compact: this means that the source can be recrafted in such
a way that cancellations due to time differences between
sound waves radiated from different regions of a given eddy
can be ignored. The sources were thought to be convected by
the flow, and Lighthill stressed that it was therefore impor-
tant to consider the Lagrangian dynamics of the turbulence
in order to understand, or predict, the spectral content of the
effective source and its sound field. There are two further
important consequences of a convected source field: more
efficient radiation in the downstream direction, and a
Doppler shift in the frequency of the radiated sound field.
2.2 Flow–acoustic interaction
The next important development where this vision of the
sound producing jet is concerned arose as a result of the
need to deal with the effect of flow–acoustic interaction,
and in particular refraction of sound away from the jet
axis—which would lead to the cone of relative silence
which is known to exist at small angles, an effect attributed
by Lighthill to a preferred orientation of the quadrupole
sources. Because all of the non-linearities of the flow
equations are lumped into the right-hand-side of Lighthill’s
equation, all flow–acoustic interaction terms are effectively
hidden in the source. Ribner (1962) first discussed this, it
was experimentally observed by Atvars et al. (1965), and
Lilley (1974) derived a modified wave equation whereby
flow–acoustic interaction effects were effectively separated
from the ‘‘production’’ mechanisms and incorporated into a
third order Pridmore–Brown wave operator. This consti-
tuted the next evolution in our vision of the mechanism by
which the free jet produces sound. The aeroacoustic system
was now considered to comprise compact, convected
sources, whose sound fields are modified by the sheared
mean-flow into which they radiate.
2.3 Temperature effects
An additional source term related to temperature fluctua-
tions was also believed to exist, and its form was assumed
2 Exp Fluids (2008) 44:1–21
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to be dipolar (see for example Fisher et al. 1973). An
extensive analysis of this source component was performed
by Tester and Morfey (1976) and Morfey et al. (1978). The
authors considered a Lilley-like description of the problem,
obtained low and high frequency solutions analytically, and
proceeded to examine the characteristics of a source term
which they considered to be due to scattering of the tur-
bulent pressure field by temperature-induced density
inhomogeneities. Their solution for the farfield sound led to
the proposition of master-spectra for the basic quadrupole,
and additional temperature-induced dipole contributions.
Put together these master-spectra gave shapes similar to
those observed experimentally for radiation in sideline
directions. Furthermore, they argued that the dipole con-
tribution would scale with velocity raised to the sixth
power.
The above description of the effects of heating were
globally accepted for the best part of 30 years. However,
recently Viswanathan (2004) has raised some serious
questions about the validity of these interpretations, and
the reliability of the experimental data which was used to
support both the existence of a dipole master spectrum
and the sixth power velocity dependence. By means of an
exhaustive study, wherein the specific effects of Reynolds
number, jet temperature, and both jet-dynamic and
acoustic Mach numbers1 were investigated, Viswanathan
(2004) was able to demonstrate quite convincingly how
the characteristic ‘‘hump’’ in the farfield spectra, tradi-
tionally attributed to the effect of the dipole master
spectrum, is in fact due to a Reynolds number effect
(heating a jet at constant Mach number leads to a
reduction in the Reynolds number). Viswanathan shows
how the effect of heat alone does not change the spectral
character of the noise radiated in sideline directions. On
the other hand the effect of heating on the sound field
radiated at small angles to the jet is shown to involve a
narrowing of the spectrum. A final important effect of
heating, observed in early experiments (Tanna et al. 1975;
Tanna 1977) and which has been confirmed by the
experiments of Viswanathan (2004), is the respective
increase and decrease in sound power radiated by the
flow which occurs when low and high velocity jets are
heated: at a critical acoustic Mach number of 0.7 the
effects of heating are reversed. Both this tendency, and
the spectral narrowing which occurs for sound radiated at
small angles to the jet axis are currently not clearly
understood and warrant further attention.
2.4 Vortex-noise analogies
Before going on to discuss the generalities of what con-
stitutes an acoustic analogy, three further important
contributions must first be cited. These are due to Powell
(1964), Howe (1975) and Mohring (1978) and comprise
acoustic analogies where the source term is formulated in
terms of the vorticity of the flow. The appeal of this kind of
analogy is largely constituted by the more intuitive feel
which it provides where the mechanisms underlying the
sound production are concerned—vortical motion is more
intuitively understood than the double divergence of a
second order stress tensor! However, in addition to this
feature of the vortex-noise analogies, there is some evi-
dence to suggest that sources so defined bring us closer to
the true physics underlying the production of sound by
unbounded turbulence (Ewert and Schroeder 2003; Cabana
et al. 2006), and, that as a result, this kind of analogy is
more robust when it comes to source modelling and its
associated inaccuracies (Schram and Hirschberg 2003;
Schram et al. 2005).
In the foregoing we have tried only to give a broad
outline of the early development of the acoustic analogy,
the interested reader can refer to the review article of
Ribner (1981) for a more exhaustive treatment of the
subject.
2.5 On the generalities of an acoustic analogy
At this point it is worth considering what precisely con-
stitutes an acoustic analogy, in order to better understand
the different forms which such a construct can take. In the
case of any of the analogies discussed above there is an
implicit linearisation about some base flow. In the case of
Lighthill-like analogies the base flow is homogeneous,
uniform, while for Lilley-like analogies the base-flow is
parallel and sheared. In each case the residual system—i.e.
the difference between the base-flow and the full com-
pressible Navier–Stokes equations—is used to define the
source, which is then considered to drive, or excite the
base-flow system. The appeal of the Lighthill-like analo-
gies is that it is relatively straightforward to compute the
response of the base-flow to such excitation; we thus see
how the trick is to define a base-flow which is described by
a partial differential equation to which either known ana-
lytical solutions exist, or which is amenable to relatively
straightforward numerical solution. The inconvenience is
that the ‘‘source’’ term must be known in full—and of
course the simpler the base-flow, the greater the complexity
of the source term if the equation is to remain exact. This
reveals an interesting situation, which is at the heart of
much controversy in aeroacoustics today: depending on the
1 Jet dynamic Mach is defined as U/cj where U is the jet exit velocity,
and cj the sound speed based on the jet temperature, acoustic Mach
number is defined as U/co, where co is the ambient temperature.
Exp Fluids (2008) 44:1–21 3
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particularities of the linearisation procedure, and the
resultant base-flow, the source definition will be different;
and so, this raises the philosophical question as to what
precisely constitutes a source mechanism. If nothing has
been discarded then the acoustic analogy is exact, the
physics of sound production is therefore described in all its
detail, and yet the space–time dynamics of what has been
called a source can vary considerably depending on the
particular analogy which has been proposed! In effect, this
situation demonstrates that in most cases there is a con-
siderable degree of redundancy (where sound ‘‘production’’
per se is concerned) in source terms so defined. In the case
of Lighthill-like analogies the redundancy of the source
term is largely manifest in the flow/acoustic effects which
are an inherent part of the source definition. A Lilley-like
analogy removes some of this redundancy by including
mean-flow/acoustic effects as part of the base flow
response; however, a certain degree of redundancy does
remain: much of the remaining source dynamic is inef-
fective in the excitation of progressive pressure modes
(perturbations which will be transmitted to the farfield):
only those source components which are acoustically
matched will couple with the farfield (Ffowcs-Williams
1963; Crighton 1975). Needless to say the Lighthill-like
analogy contains this redundancy in addition to the afore-
said flow/acoustic effects. In both Lighthill- and Lilley-like
analogies the solution procedure for the base-flow response
involves an inherent ‘‘sorting-out’’ of the source redun-
dancies: in both systems the Greens function solution for
the base-flow response translates a filtering operation
which only passes acoustically matched source compo-
nents. This filtering amounts to the radiation criterion
x = jc (Ffowcs-Williams 1963; Crighton 1975).
The implication here is that none of the aforementioned
analogies are optimal—the job of describing the physics of
sound production is essentially shared between the source
term (the excitation) and the response of the differential
equation which describes the base-flow. This is one of the
reasons for the considerable controversy which surrounds
the question of what constitutes a meaningful source defi-
nition. Recognising this, Goldstein (2003) endeavoured to
put the acoustic analogy on a more general footing, and
demonstrated indeed how the procedure can be generalised
such that a linearisation can be performed about any given
base-flow. He demonstrates how Lighthill- and Lilley-like
analogies are just special cases in a more general frame-
work, and how in fact the base-flow can comprise an
unsteady system, e.g. a URANS-type solution to the
Navier–Stokes equations, or an incompressible Navier–
Stokes solution. Indeed, in a later paper Goldstein (2005)
proposes an acoustic analogy, which, were it possible to
achieve, might constitute an optimal description of the
problem, whence the source definition would comprise no
redundancy and would thus provide a true source defini-
tion. Unfortunately, in all but a periodic, homogeneous
unsteady flow system (such as homogeneous, isotropic
turbulence in a periodic cube), such a procedure will vio-
late locality constraints, and so in the case of flows of
practical interest it is unlikely that this procedure can be
applied. Furthermore, the proposed method involves a fil-
tering operation based on the criterion x = jc, which is
simply a spectral expression of the radiation criterion for
small amplitude fluctuations propagating in an irrotational
medium at rest or in uniform motion; it is uncertain that
such a filtering operation will isolate acoustic disturbances
in a more complex rotational flow system.
We will later see how these questions are finally
becoming, and indeed must be made the primary focus of
the experimental approach. The experimentalist must
understand how to relate what is measured to something
which can be meaningfully considered to describe the
sound production mechanism. As we will see, even if we
manage to measure or compute the entire space–time
structure of the Lighthill stress tensor, or other so-called
‘‘source’’ quantity, the problem is far from solved.
An alternative means by which the physics of aerody-
namically generated sound can be described involves the
use of rapid distortion theory; however, in a 1984 review
article Goldstein (1984) provides an excellent account of
this kind of approach and so we will here omit any detailed
description of the subject.
2.6 Coherent structures
As we have seen, our early ideas of the sound production
mechanisms in jets were based on a system of randomly
distributed eddies, convected with and radiating into a
given mean-flow. This view was to change radically over
the course the 1960s and 1970s when the turbulence
community began to recognise the existence of a more
organised underlying structure in free shear-flows.
Needless to say the aeroacoustics community was quick
to realise that this could have significant implications
where the corresponding sound production mechanisms
are concerned. A few researchers were to address this
issue in the 1960s. Bradshaw et al. (1964a, b) observed
large, organised eddies in the near-nozzle region of the
round jet, and Mollo-Christensen (1967) discussed the
possibility that such structures might play an important
role in the production of sound. However, it was in the
early 1970s, with the work of Crow and Champagne
(1971), Lau et al. (1972), Fuchs (1972) and Brown and
Roshko (1974) that the aeroacoustics community really
began to focus on the implications for sound production
by free jets.
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Michalke and Fuchs (1975), in an analytical develop-
ment based on Lighthill’s theory re-cast in cylindrical
coordinates, represented the source in terms of its azi-
muthal Fourier modes, and showed thence that the lowest
order modes would be the most efficient producers of
sound, this efficiency depending strongly on the axial
coherence of the source. The existence of strong azimuthal
coherence in the sound field radiated by the round jet
(Michalke and Fuchs 1975; Maestrello 1977; Fuchs and
Michel 1978; Juve et al. 1979) provided evidence that the
source mechanisms might indeed comprise such azimuth-
ally coherent vortex-ring-like structures; and while Bonnet
and Fisher (1979) were to warn against such overhasty
inferences regarding the source structure based purely on
the far sound field—they demonstrated that the coherence
of the sound field radiated by a ring-like structure, coherent
or otherwise, depends largely on the Helmholtz number,
and how an azimuthally incoherent ring-source could in
fact produce an azimuthally coherent sound field for cer-
tain frequencies—Fuchs (1972) and Armstrong et al.
(1977) demonstrated that in fact the flow does comprise
such azimuthally coherent structures, these observations
being based on two-point pressure and velocity measure-
ments in the rotational region of the jet. Where the axial
coherence of the jet structure is concerned Chan (1974)
showed that the growth and decay of pressure disturbances
is similar to that predicted by linear hydrodynamic stability
theory (Michalke 1964, 1965).
The identification of such a deterministic underlying
structure triggered considerable interest in alternative
means of modelling source mechanisms. The likeness of
the coherent flow dynamics of moderate-to-high Reynolds
number jets to the linear instabilities observed in laminar
flows led to attempts to use linear instability theory to
predict jet noise. Tam (1972) first presented such an
approach for supersonic jets in 1972 by considering the
linear instability of an infinitely thin shear-layer in a par-
allel mean-flow. Liu (1974) attempted to better integrate
the effects of a spreading mean-flow and a fine-grained
background turbulence, which would respectively sustain
and dissipate the large-scale instability.2 The near pressure
field thus predicted showed good qualitative agreement
with experimental measurements. Ffowcs-Williams and
Kempton (1978) studied the sound production capability of
both a wavy-wall type instability and a vortex-merger
event using an ad hoc description of the said mechanisms
and a Lighthill source formulation. For both cases the rapid
amplification, saturation and decay of the fluctuations
associated with such mechanisms were shown to be
important in the production of sound. Moore (1977) pro-
vided experimental evidence for the importance of
coherent structures in the production of jet noise, while
Dahan et al. (1978) subsequently demonstrated, experi-
mentally, for a hot jet, that 50% of the sound energy
radiated to the farfield could be attributed to the dynamics
of coherent flow structures. An early attempt to address the
question numerically was made by Gatski (1979).
By the end of the 1970s, both the existence and the
importance of coherent source structures had been estab-
lished, experimentally and theoretically. It is worth
mentioning that this identification of the importance of
coherent structures in the production of sound was to
produce a divide in the aeroacoustics community, as the
existence of such structures cast some doubt on the validity
of the earlier vision of a random distribution of compact,
convected quadrupoles. While there was no question of
entirely eliminating the possibility of such source mecha-
nisms, it was clear that this picture was not complete. An
interesting exchange between Fuchs (1978) and Ribner
(1978) provides a nice resume of some of the contentious
issues.
Subsequent developments in the modelling of source
mechanisms associated with the coherent component of the
free jet have been largely tied to the supersonic scenario
(e.g. Morris 1977; Tam and Morris 1980; Tam and Burton
1984; Tam and Chen 1994), and indeed linear stability
theory can be used to provide a reasonable quantitative
prediction of the sound field radiated, via Mach wave
mechanisms, by the most amplified linear modes in
supersonic jets, as shown by Tam and Burton (1984), Tam
et al. (1992), and Tam and Chen (1994). However,
Mohseni et al. (2002) have shown, by means of numerical
simulations comprising both linear and non-linear Navier–
Stokes solutions, that for off-peak frequencies discrepan-
cies between the linear and non-linear solutions are
considerable, indicating that the linear theory is not suffi-
cient to account for all of the subtleties of Mach wave
radiation. For subsonic jets, similar theoretical work has
been performed by Mankbadi and Liu (1981, 1984),
wherein instabilities computed using a combination of
linear and non-linear theory—the shape function is derived
from local inviscid linear theory while an axial amplitude
function is obtained from non-linear theory—are used to
construct source terms using a reworking, by Michalke and
Fuchs (1975), of the Lighthill (1952) theory. Predictions of
the spectral and directive character of the acoustic field
radiated by spatially stationary, coherent source mecha-
nisms were found to reproduce many of the observed
subsonic jet noise characteristics. Axisymmetric and
2 This was based on a three-way split of flow quantities into time
averaged, phase-averaged and random components (associated,
respectively, with the mean flow, the large-scale instability and the
fine-scaled, random turbulence) which was first used by the turbu-
lence community in order to understanding the dynamics of coherent
structures in free shear flows (see Hussain and Reynolds 1970 for
example).
Exp Fluids (2008) 44:1–21 5
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helical source modes were found to resemble longitudinal
and lateral quadrupoles; peak radiation was found to occur
at small angles to the jet axis, at Strouhal numbers of the
order of 0.3, and the linear, ‘‘shear-noise’’ mechanism, was
found to dominate. A particularly attractive feature of their
approach is that energy transfers between the mean-flow,
the large-scale instability, and the fine-scale turbulence are
accounted for, and in this the model is physically more
complete than the models which are typically used for
supersonic predictions, even if the authors neglected the
finescale turbulence in the source integral. Discrepancies
between predictions and experimental results were attrib-
uted to this neglect of the fine-scale component, however it
is likely that the observations of Mohseni et al. (2002) may
also be applicable here.
The possibility of the existence of both a large-scale
coherent component and a more random small-scale com-
ponent was further investigated by Tam et al. (1996) for a
perfectly expanded supersonic jet, and this led Tam (1998)
to propose two similarity spectra, related to each of the two
mechanisms. These were shown to agree well with data
taken from a large number of supersonic jet noise experi-
ments, and Viswanathan (2002) has shown how subsonic
jet noise spectra also fit these shapes. However, the
essential features of the physics underlying the two kinds
of mechanism in the subsonic jet remain unclear to this
day, and thus in terms of source modelling this small-scale-
random/large-scale-coherent source duality remains a
central problem. An interesting interpretation of this source
duality has recently been provided by Goldstein and Leib
(2005), who show that the Greens function solution for a
Lilley-like acoustic anology comprises two distinct terms,
each of which filters the source dynamic in a different way;
again the conceptual difficulty alluded to earlier, wherein
the physics of the sound production problem is shared
between the ‘‘source’’ and the base-flow ‘‘response’’, arises
here: the authors argue that the base-flow responds in two
different ways to the turbulence dynamic: a low frequency
response which is greatest at shallow angles to the jet axis,
and a high frequency response which dominates at larger
angles. The former component corresponds to linear
instabilities associated with the homogeneous solution for
the base-flow equation, and so is argued to be synonymous
with large-scale flow instabilities, although the authors do
make the further comment that the said instabilities ‘‘may
not actually correspond to any physical flow structure’’—
an apposite remark in view of the aforesaid conceptual
difficulties which arise when it comes to ‘‘speaking of’’
source mechanisms.
Where the small-scale-random component is concerned
the traditional Lilley or Lighthill approaches, which
involve assumptions of convected, compact quadrupoles,
may be well adapted. However it is unclear how individual
contributions from the coherent and random turbulence
components to the moving-frame two-point space–time
velocity correlation tensors (see Sects. 2.1, 3.1 for related
discussion) can be separately identified experimentally.
Indeed the form of the correlation tensor is quite likely
dominated by the large-scale, coherent flow dynamics. This
problem presents a challenge for the future. On the other
hand, where the coherent component is concerned there is
no real consensus as to the essential mechanisms involved.
The early candidates were vortex-pairing and/or wavy-wall
type instabilities; Coiffet et al. (2006) give experimental
evidence supporting the existence of this kind of mecha-
nism in the region upstream of the end of the potential core,
and demonstrate that the production mechanism is a linear
one. On the other hand, Kopiev and Chernyshev (1997)
have provided an analytical demonstration of how the ei-
gen-oscillations of a single vortex structure can constitute
an efficient octupole sound production mechanism, which
presents a directivity similar to that produced by a jet
(Kopiev et al. (1999, 2006). There is also a considerable
body of experimental and numerical evidence suggesting
that a particularly violent event associated with the collapse
of the annular mixing-layer at the end of the potential core
may constitute the dominant sound production mechanism.
The early causality methods (discussed in Sect. 3.2.1)
identified this region of the flow as the dominant source
region, and an experimental study undertaken by Juve et al.
(1980) showed how sound producing events in this region
are characterised by high levels of intermittency: sudden
decelerations near the end of the potential core, thought to
be related to fluid entrainment on the upstream side of ring-
like coherent structures, were postulated as a possible
mechanism. More recently Guj et al. (2003) and Hileman
et al. (2005) have provided further experimental evidence
for intermittent noise producing events in this region of the
flow. Numerical simulations which further support the
existence of such a source mechanism have been per-
formed by Bogey et al. (2003) and Viswanathan et al.
(2006). The former work shows how large amplitude sound
waves are generated by the intrusion of structures into the
potential core region, while in the latter work a strong,
inherently directive, spatially stationary sound source is
again identified just downstream of the end of the potential
core.
2.7 Summary
The foregoing gives an overview of the different ideas
which currently exist regarding the sound production
mechanisms in free jets. Jets are believed to comprise two
kinds of mechanism: one related to the small-scale, random
flow eddies, which are compact, convected, and behave as
6 Exp Fluids (2008) 44:1–21
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quadrupole sound sources; and another related to the
coherent flow dynamic, which is variously considered to
produce sound via vortex-pairing, vortex eigen-oscilla-
tions, quasi-irrotational instability or wavy-wall-like
mechanisms, and a violent intermittent flow dynamic in the
transition region of the flow. However, as discussed in the
introduction, it remains unclear whether this hypothesis of
two distinct mechanisms is justified. Goldstein’s perspec-
tive suggests that one and the same ‘‘source’’ mechanism
may simply be coupling with the farfield in a highly
directive fashion, and such that an angle-dependent fre-
quency selection occurs. Furthermore, the idea that the
mechanisms might be associated with disparate scales is
not so clear, as there is a considerable degree of overlap
between the spectral shapes associated with each of these
mechanisms (i.e. those observed at 90� and 30� to the jet
axis).
We defer further discussion on this to the next section,
where we will look more closely at the various measure-
ment and analysis strategies which have been used to
extract pertinent information concerning the various sound
production mechanisms believed to exist in the unbounded
round jet.
3 Experimental methodologies and source modelling
Despite impressive recent progress in our capacity to solve
the flow equations numerically, such approaches remain
seriously limited in terms of the kinds of Reynolds num-
bers which can be achieved, and the precision with which
the turbulent motion of a heat-conducting, viscous, com-
pressible fluid can be resolved. Where jets are concerned
the extremely thin boundary layers (upstream of the exit
plane) and initial shear-layers require prohibitively large
numbers of mesh points. This leads to severe restrictions in
terms of the run-times which can be obtained, and so it is
generally difficult to obtain fully converged statistics. The
experimental approach, where the flow equations are per-
fectly solved by the flow, is therefore presently essential if
we are to arrive at an integral understanding of the sound
production problem for the kinds of flows which are of
practical interest.
In this section we wish to provide an account of the
evolution of the different experimental approaches which
has accompanied the developments outlined above. Such
evolution is driven both by improvements in measurement
technology, and, possibly more importantly, by the evo-
lution of our understanding of the mechanisms which
underlie the production of sound by a jet. As the various
visions of the sound-producing jet appeared, experiments
were designed in order to access the pertinent information
where sound production is concerned. Needless to say this
process is ongoing, and recent developments are bringing
us ever closer to directly accessing the ever elusive jetnoise
‘‘source’’ dynamic.
3.1 Two-point statistics
Within the framework of the original acoustic analogies,
the sound power radiated from a jet comprising randomly
distributed, compact, convected quadrupole sources is
related to the fourth order, spatiotemporal velocity corre-
lation tensor. By means of a Reynolds decomposition of the
velocity field, this can be shown to comprise second, third
and fourth order terms. The third order terms are generally
neglected as they integrate to zero in homogeneous, iso-
tropic turbulence.3 The second and fourth order terms are
related to linear and quadratic pressure production mech-
anisms, respectively,4 the so-called ‘‘shear-’’ and ‘‘self-
noise’’ mechanisms (Lighthill 1954; Ribner 1969) (or fast
and slow pressure terms in the turbulence community).
With an assumption of quasi-normal joint probability of the
turbulence statistics [this assumption has been shown to be
justified, experimentally by Seiner et al. (1999), and
numerically by Freund (2003) using DNS] the fourth-order
quantity can be expressed in terms of the second order
velocity correlation tensor, and so early experiments
designed to extract information related to the source
mechanisms via direct turbulence measurements targeted
the two-point velocity correlation (e.g. Davies et al. 1963;
Fisher and Davies 1964; Chu 1966). Due to limited mea-
surement capabilities, such experiments were generally
limited to a study of only one of the nine components of the
correlation tensor (the axial component); assumptions of
isotropy and homogeneity were then invoked in order to
model the remaining terms. The three quantities of interest
are the integral space scale, the Lagrangian integral time
scale and the convection velocity. Armed with these and an
isotropic, homogeneous turbulence model—taken for
example from Batchelor (1953)—it is possible to make jet
noise predictions, and indeed this kind of approach is still
at the heart of many current noise-prediction procedures.
Progress where this kind of approach is concerned has
involved a more complete measurement of the said two-
point tensor by means of PIV and LDV (e.g. Bridges 2002;
Chatellier and Fitzpatrick 2006; Kerherve et al. 2004,
2006). And in terms of improvements in subsequent
modelling the focus has generally been on the inclusion of
3 It should be noted that the turbulence in a round jet is neither
isotropic nor homogeneous, and so neglect of the third order term may
constitute a dangerous oversimplification.4 By pressure production terms we mean terms such as are found on
the right-hand side of a Poisson’s equation for the pressure field in an
incompressible turbulence field.
Exp Fluids (2008) 44:1–21 7
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more flow physics. Models are frequently based on
assumptions of isotropic, homogeneous turbulence. As the
jet is clearly neither, a certain effort has gone into devel-
oping more realistic models which include more of the
observed flow physics. Goldstein and Rosenbaum (1973)
examined the role of anisotropy by means of models based
on the theory of axisymmetric turbulence of Chandrasekhar
(1950). Later work on the same lines includes the use, by
Khavaran (1999), of the axisymmetric turbulence model to
deal with anisotropy and to predict the sound radiated from
a jet using data obtained from a RANS computation. Jordan
and Gervais (2005) combined a similar turbulence model
with a technique developed by Devenport et al. (2001) in
order to deal with the inhomogeneity of the jet structure,
and a direction-dependent length-scale was proposed in
order to deal with the anisotropy of the turbulence; jet noise
predictions were then made using data obtained from two-
point LDV measurements.
Other progress in this kind of statistical modelling
includes the use of frequency-dependent space–time scales
(Self 2004; Kerherve et al. 2006). Khavaran and Bridges
(2005) have shown how the shape of the temporal part of
the two-point velocity correlation can play an important
role in the accuracy of predictions, exponential forms being
more appropriate than the traditionally used Gaussian
forms, while Jordan et al. (2004) suggest that it is also
important to model the curvature of the correlation function
close to zero. In order to do so, without losing the expo-
nential global decay, they proposed a function obtained via
convolution of exponential and Gaussian forms, charac-
terised, respectively, by the integral and Taylor scales of
the flow: again emphasis is here laid on the inclusion of
physical flow quantities, rather than the use of empirical
constants to get the right answer.
3.2 Simultaneous flow–acoustic measurements
As discussed earlier, there exists a degree of uncertainty
when it comes to defining the sound production mecha-
nisms in unbounded turbulence. This means that there is a
corresponding uncertainty when it comes to designing
experiments aimed at understanding the dynamics of such
mechanisms in a given turbulent flow.
An experimental approach which can help shed some
light in this matter involves the synchronous recording of
fluctuations in both the near field of the flow—which may
include both rotational and irrotational regions—to which
the source mechanisms are confined but largely swamped
by acoustically un-important hydrodynamic fluctuations,
and in the far acoustic field, where only the source signa-
ture remains. By means of such a measurement the causal
relationship between the flow/source dynamic and its
acoustic effect (the sound field) can be assessed by corre-
lation or other appropriate signal processing techniques.
While there is little doubt that the appropriate farfield
quantity to target is the fluctuating pressure, the pertinant
flow/source quantity is not so obvious. Experiments can
either be guided by an acoustic analogy, or causal rela-
tionships can be sought using whatever flow information it
is possible to obtain: indeed this is often the decisive factor
when it comes to performing such an experiment: we
cannot access the full space–time dynamics of the flow; we
have different tools, each permitting of partial access to
different flow quantities.
3.2.1 The causality method
Early experiments were guided by the Lighthill analogy,
and in particular by the identification of linear and qua-
dratic (‘‘shear-’’ and ‘‘self-noise’’) quadrupole source
mechanisms on one hand, and the simple pressure source
mechanisms proposed both by Ribner (1962) and Powell
(1963) on the other. Two variants of the causality method
thus appeared in the early 1970s as a result of these dif-
ferent source descriptions. The first can be attributed to
Siddon and Rackl (1972) and was based on cross-correla-
tions between in-flow pressure fluctuations and those
radiated to the farfield. The second approach, first pre-
sented by Lee and Ribner (1972), was based on correlating
Reynolds stress fluctuations with the farfield pressure.
Before going on to discuss the principal results, a few
words are appropriate concerning the importance of this
particular approach.
The appeal of the causality method derives from the fact
that the farfield pressure autocorrelation—which consti-
tutes a measure of the sound energy radiated from the
flow—can be formally related to the source–farfield cor-
relation, which can in turn be formally related to the
source-source correlation which comprises the integrand in
the farfield solution of Lighthill’s wave equation. Such
causality-correlations are thus more than a mere ad-hoc
test for a cause–effect relationship. Indeed, within the
framework of Lighthill’s acoustic analogy, a two-point
source–farfield correlation, hS(x,t)p(y, t + s)i, amounts to a
quantitative measure of the local contribution from source
activity at a point x in the jet, to the farfield sound intensity
measured at y. By integrating the source–farfield correla-
tions over the entire jet volume, taking care to correctly
account for negative source contributions, the total sound
power radiated by the jet is retrieved. The causality method
is thus seen to be no less than a high-precision source
localisation technique, which identifies the structure of the
coupling mechanism via which the largely acoustically
ineffective jet dynamics drive the farfield pressure. This is
8 Exp Fluids (2008) 44:1–21
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an extremely important point in view of the earlier dis-
cussion related to the difficulty of identifying something
which can be meaningfully referred to as a ‘‘radiating’’
source: because of the formal identity between the source–
farfield correlation and the integral solution of Lighthill’s
equation, the filtering operation by which the said solution
sorts and extracts acoustically matched source activity is
inherently present in the source–farfield correlations.
As different researchers implemented the causality
method a number of important improvements were made,
and some interesting findings reported. The first experi-
ments availed of hot-wire, hot-film, and in-flow pressure
probes to sample fluctuations in the flow field. Lee and
Ribner (1972) used a hot film to correlate the square of the
fluctuating velocity with the farfield pressure of a Mach 0.3
jet. This was done using only the velocity component in the
direction of a farfield microphone (which was located at
40� to the jet axis), in accordance with a formulation of the
Lighthill equation proposed by Proudman (1952). Scharton
and White (1972) alternatively studied correlations
between pressure measurements effected in the rotational
region of a sonic jet and in the farfield at 30� to the jet axis.
Seiner (1974) and Seiner and Reethof (1974) performed a
similar experiment to that of Lee and Ribner (1972), in a jet
at Mach 0.32 using a hot-wire, but where both the linear
and quadratic velocity fluctuations were considered. In this
way it was possible to assess contributions from the so-
called ‘‘shear-’’ and ‘‘self-noise’’ mechanisms. Again fil-
tered correlations were computed, whence it was shown
that the frequency of the sound radiated from the jet is a
function of axial position: high frequencies were found to
be radiated from upstream positions, lower-frequencies
from downstream positions. The linear (‘‘shear-noise’’)
mechanism was shown to dominate the quadratic (‘‘self-
noise’’) mechanism by 13 dB, and the transition region of
the jet (downstream of the end of the potential core) was
shown to be dominant in the production of sound.
A difficulty with this kind of approach arises due to the
strong possibility that the in-flow probe is generating more
sound than the sources it is designed to measure.
Researchers thus took to designing experiments where
probe contamination was minimised. Schaffar (1979) used
LDV to measure the axial component of the velocity
fluctuations in a high Mach number jet (M = 0.97), and by
correlating the linear source component with the farfield
pressure was able to conclude, in agreement with Seiner,
that ‘‘nearly all of the far field noise measured at 20� and
30� to the jet axis’’ is produced by linear, ‘‘shear-noise’’
mechanisms present in the transition region of the flow,
between 5 and 10 diameters downstream.
Juve et al. (1980) also performed an experiment where
efforts were made to minimise probe contamination. A hot-
wire probe was designed such that the hotwire support
structure exposed to the turbulent flow comprised only four
100 lm diameter support wires. Acoustic measurements
were made using microphones located at 30� to the jet axis.
In addition to time-averaged correlations, the authors
studied instantaneous correlations, and they emphasised
that the exact time-delay associated with transmission from
source to observer must be appropriately accounted for if
cancellation effects are to be correctly captured. These
correlations provide a means of assessing the instantaneous
sound emission associated with the ‘‘shear-noise’’ source
term, and led to a number of important observations
regarding the nature and localisation of the sound pro-
duction mechanisms. The dominant source was again
shown to be localised in the transition region, downstream
of the end of the potential core; it was found to be non-
compact and related to the coherent dynamic of the jet;
and, finally, it was shown to be highly intermittent, with
50% of the sound being generated in 10–20% of the time.
This last point is an extremely important one where source
models are concerned. In addition to a confirmation of the
non-compactness of the source mechanism which had been
suggested by earlier research, as discussed in Sect. 6, the
observed intermittency of the source suggests that the
statistical source models, which are based on the existence
of compact turbulent eddies in an isotropic, homogeneous
field (where source terms associated with the third order
statistical moments are considered negligible), are insuffi-
cient for an accurate description of the full source dynamic.
Schaffar and Hancy (1982), following the earlier work
of Schaffar (1979), used an LDV system to measure
velocity components in the direction of farfield micro-
phones at 30�, 45� and 60� to the jet axis. It was thereby
possible to better understand the directivity of the ‘‘source’’
mechanisms. Both the linear and the quadratic components
were found to be active in the transition region of the flow,
between 4 and 11 diameters downstream of the exit. The
linear term was found to dominate considerably, with over
70% of the radiated energy being emitted at angles smaller
than 45� to the jet axis; the quadratic term was found to
contribute of the order of 15%; for sound emitted at angles
greater than 60�, the linear term was found to be ineffec-
tive, while the quadratic term only contributed a few
percent of the radiated energy. The authors again evoked
the importance of using the exact time-delay when per-
forming source–farfield correlations, such that source
cancellation effects are correctly taken into account.
Panda et al. (2005) have more recently performed a
similar experiment using a novel technique, based on
molecular Rayleigh scattering, which permits simultaneous
measurement of both unsteady density and velocity. Such a
measurement allows the Lighthill stresses to be measured
in full, without the incompressibility assumption. The work
of Cabana et al. (2006) and George et al. (2007) suggests
Exp Fluids (2008) 44:1–21 9
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that terms associated with the unsteady density may com-
prise the most fundamental event where the source
mechanisms are concerned, and so direct experimental
access to such quantities is of considerable interest. In-flow
measurements of quu, qvv, q, u and v were performed in
subsonic and supersonic jets, synchronously with farfield
pressure measurements at 30� and 90� to the jet axes by
Panda et al. (2005). Correlation levels in the subsonic flows
were of the order of 1–2% (considerably lower than in the
supersonic flows). The highest correlations were obtained
from the quu, q and u measurements. As the measurements
were performed on the jet axis, the failure of the v com-
ponents to correlate led to the conclusion that axisymmetric
instability waves/coherent structures were the primary
sound producers in the supersonic jets. The highest corre-
lations were observed for in-flow measurements performed
just downstream of the end of the potential core, consistent
with many previous experiments. For in-flow measure-
ments in the mixing-layer region, at r/D = 0.45,
correlations were found to be negligible in the subsonic
flows. It should be pointed out that this may be partly due
to the masking effect of the more random turbulence—the
random component of the turbulence may be sufficiently
energetic to swamp the part of the coherent dynamic which
is correlated with the farfield—we will see later how there
is a strong coherent dynamic in this region of the subsonic
jet, which does generate sound, but whose signature is
strongest on the low and high speed sides of the mixing-
layer, where the masking effect of the random turbulence is
less severe.
3.2.2 Flows dominated by coherent structures
In the previous subsection techniques which were strongly
rooted in the acoustic analogy were considered, and while
the associated physical picture was frequently that of a
convected field of compact quadrupoles, many of the
conclusions pointed to non-compact source mechanisms
associated with the coherent dynamics of the flow. Rec-
ognising this, researchers began to address the question of
how to study the underlying mechanisms in more detail.
Experimentalists thus took to contriving flow systems
which were dominated by deterministic coherent motion.
One approach is to use an acoustic excitation to lock a low
Mach number round jet into a regular flow pattern. By
forcing at the most unstable frequency of the flow, a system
of coherent vortex structures can be produced, where the
roll-up and pairing phases are fixed in space. Moore
(1977), Kibens (1980), Laufer and Yen (1983), Arbey and
Ffowcs-Williams (1984), Bridges and Hussain (1992),
Ghosh et al. (1995) and Fleury et al. (2005) have all
studied such coherent-structure-dominated flows.
In addition, Laufer and Yen (1983) performed syn-
chronous flow–acoustic measurements in both excited and
un-excited flows with a view to relating the flow dynamics
to the radiated sound. However, their work differed from
the causality approaches described above in that they did
not place themselves within the framework of any under-
lying aeroacoustic theory; they simply observed the
simultaneous behaviour of the flow and its radiated pres-
sure field. From measurements restricted to the first
diameter of the flow, they found that the turbulent velocity
and the nearfield pressure—measured in the irrotational
entrainment region—are linearly related, while a quadratic
relationship exists between nearfield and farfield pressures.
They observed that for both the excited and unexcited
flows ‘‘the acoustic sources are not convected even though
they are being generated by moving disturbances in the
jet’’, and the quadratic relationship between the nearfield
and farfield measurements led to the conclusion that the
source mechanism could be associated with the non-linear
saturation of unstable wave amplitudes occurring near the
vortex-pairing locations. Clearly the observed phenomena
violate some of the assumptions on which the original
source models were based: if the source is not convected
there can be no convective amplification and no Doppler
shift, and yet they observed a superdirective radiation
pattern! Non-linear mechanisms associated with vortex
pairing mechanisms were also argued by Stromberg et al.
(1980) to be dominant in the production of sound by low
Reynolds number round jets. They used a novel experi-
mental approach, pioneered by Morrison and McLaughlin
(1979) for the study of supersonic flows, which involves
exhausting high speed jets into an anechoic vacuum
chamber. By virtue of the low Reynolds number thus
obtained, coherent flow patterns in high Mach number, un-
excited flows, could be studied.
The apparent contradiction, between these observations
of a non-linear relationship between the nearfield dynamics
and the farfield sound, and the conclusions from the cau-
sality approach which indicate that the linear source term is
dominant, may be an indication that such vortex-pairing (or
non-linear instability wave interactions) do not constitute
the dominant mechanism in unexcited, high Reynolds
number flows. It is possible that in an unexcited jet the
coherent dynamic is not coherent enough to produce such
‘‘clean’’ quadratic interactions. Further investigation of this
point would be useful.
3.2.3 Conditional averaging
We have seen how synchronous flow–acoustic measure-
ments led to a number of important observations with
regard to the sound production mechanisms in free jets:
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the dominant sound producing region of the flow, where
both linear and quadratic mechanisms are concerned, was
found to be the transition region downstream of the col-
lapse of the potential core, and at least some component of
the source mechanism was found to be non-compact,
spatially stationary—and therefore inherently directive—
and strongly intermittent. One important implication of an
intermittent source is that second order averaging tech-
niques may be missing the essential character of the sound
production event. With this in mind Guj et al. (2003)
performed synchronous flow–acoustic measurements with
a view to analysing the relationship between the dynamics
of the unsteady intermittent structures in the transition
region of the jet and the sound they radiate. Conditional
ensemble averaging was implemented, peak events in the
acoustic signature being used as a conditional trigger.
Intermittent source activity was identified between seven
and nine diameters downstream, and the characteristic
sound production event found to be characterised by a
cusp-like signature, as previously observed by Juve et al.
(1980) (cf. Sect. 3.2.1) and later by Hileman et al. (2005).
The methodology implemented by Hileman et al. (2005) is
very similar to that of Juve et al. (1980) and Guj et al.
(2003), but in the place of single-point flow measure-
ments, high-speed flow visualisations were performed
using a PIV system. In similar fashion to the work of Guj
et al. (2003), the farfield acoustic signal was used to sort
the flow images into noisy and quiet ensembles. The signal
processing tool used in this case was proper orthogonal
decomposition, which was applied to both ensembles, and
thus used to understand the characteristic features com-
prised by the images associated with periods of high noise
production and with periods of relative quiet. The transi-
tion region was once again identified as dominant in the
production of sound, and a cusp-like signature again
shown to characterise the intermittent sound production
events.
3.2.4 Summary
The evolution of synchronous flow–acoustic measurements
has primarily involved improvements in measurement
technology, and has been marked by a movement away
from the theoretical groundings which typified the early
causality methods. As discussed in Sect. 2.5, the concep-
tion of an acoustic analogy has seen some evolution and the
new formulations which will now be possible should be
conducive to a return to more theoretical groundings.
Indeed, the experiment will be an interesting testing ground
for evaluation of the different source definitions which the
new approaches provide. And of course, the new source
definitions will constitute a continued challenge to the
experimentalist to extract the associated pertinent infor-
mation. We will return to this point a little later.
3.3 Nearfield pressure measurements
Another means of investigating the dynamics of a free
jet—which was first implemented in the early 1950s—
involves the use of microphones located in the irrotational
region just outside the jet periphery. Although this kind of
measurement presents numerous advantages, it also raises
considerable interpretational difficulties. On one hand
pressure is a scalar quantity, the measurement is non-
intrusive, and as the smaller turbulence scales are ineffi-
cient in driving the pressure field in this region of the flow,
such measurements involve a natural filtering of these, and
are thus conducive to a study of the large-scale, coherent
dynamics of the jet. On the other hand, as discussed in
Tinney et al. (2006b), interpretation of the measured fluc-
tuation in terms of the underlying turbulence and its sound
source mechanisms is far from straightforward. There is
always an uncertainty as to precisely how much informa-
tion has been filtered out with respect to the pressure
signatures at the heart of the turbulent flow. A further
difficulty arises related to the fact that the measurement
comprises contributions from both ‘‘hydrodynamic’’ and
‘‘acoustic’’ pressure fields. If these issues are not appro-
priately dealt with, such measurements can be easily
misinterpreted.
Early theoretical work in this field was undertaken by
Franz (1959) and Ollerhead (1967), both of whom made
detailed studies of the nearfield solution to Lighthill’s wave
equation. This solution comprises rapidly decaying terms
related to the highly energetic reactive pressure field which
exists close to an acoustic source, but which does not reach
the farfield due to its non-progressive nature. The irrota-
tional nearfield of an unbounded jet is dominated by such
pressure fluctuations, which, on account of their rapid
spatial decay, present a relatively local information where
the large-scales of the underlying turbulence are concerned.
An alternative analytical approach, used for example by
Howes (1960), involves treating the pressure fluctuations
as entirely incompressible. The characteristics of the
nearfield pressure are then described by a Poisson equation,
whence Howes derived expressions for the evolution of the
nearfield pressure rms and found reasonable agreement
with experimental measurements.
Early experiments by Mayes et al. (1959), Howes
(1960), Mollo-Christensen (1963) and Keast and Maidanik
(1966) involved one and two-point measurements from
which the axial evolution of the first and second order
moments, and the two-point pressure correlations were
obtained. Howes (1960) appears to have been the first to
Exp Fluids (2008) 44:1–21 11
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consider the subsonic jet, the near pressure field of which
was found to comprise an amplification, saturation and
decay of the fluctuation amplitudes, as predicted by the
theoretical approach, mentioned above, which was based
on incompressible pressure fluctuations and jet similarity
relations. Mollo-Christensen (1963) performed two-point
pressure correlations, using probes separated both axially
and in azimuth. The shape of the space–time correlations
thus obtained suggested a harmonic travelling wave,
weighted by a Gaussian envelope and an exponential axial
decay. A striking feature identified by these early experi-
ments, and in particular that of Mollo-Christensen (1963),
was the coherent nature of the near pressure field: as dis-
cussed above it presents a natural filter, which extracts the
coherent flow dynamics from a background of more ran-
dom turbulence. Despite the fact that this filter is presently
poorly understood, such measurements are nonetheless
attractive where the small-scale/large-scale source duality
discussed earlier is concerned, and this kind of experiment
may constitute a valuable means for understanding these
source mechanisms.
A problem evoked earlier with respect to source defi-
nitions is the redundancy present in many of these, and in
particular with respect to the non-radiating components. In
a subsonic jet much of the flow dynamic is non-radiating,
and so some care is required when the nearfield signatures
are considered in terms of the underlying, radiating
source. Keast and Maidanik (1966) provide a nice
description of this difficulty where the near pressure field
is concerned. However, until recently (Tinney et al.
2006b) this point, as well as the question of the compo-
sition of the nearfield in terms of ‘‘hydrodynamic’’ and
‘‘acoustic’’ components (e.g. Arndt et al. 1997; Millet and
Casalis 2004; Coiffet et al. 2006), have been largely
overlooked in nearfield studies.
In an analytical development based on the unsteady
Bernoulli equation and a quadrupole solution to the wave
equation, Arndt et al. (1997) obtained predictions for the
spectral character of nearfield pressure fluctuations of a
subsonic jet, and the ‘‘hydrodynamic’’ and ‘‘acoustic’’
spectral regimes thus predicted agreed well with mea-
surements. A Helmholtz number of kr = 2 was found to
mark the passage from ‘‘hydrodynamic’’ to ‘‘acoustic’’
dominance. Harper-Bourne (2004) and Coiffet et al. (2006)
found values of kr = 1 and kr = 1.3, respectively, while
Guitton et al. (2007) have more recently derived an
empirical relationship which accounts for the velocity
dependence of the ‘‘hydrodynamic’’–‘‘acoustic’’ demarca-
tion: this empirical law accounts for the different velocity
dependence of the hydrodynamic and the acoustic com-
ponents of the nearfield pressure intensity, which scale,
respectively, as U4 and U7. In terms of the relationship
between the ‘‘hydrodynamic’’ and ‘‘acoustic’’ components
of the near pressure field, further light has been shed on the
matter by Coiffet et al. (2006), who by means of an axially
aligned linear nearfield array, demonstrated a causal link
between the two fluctuating fields, manifest in the form of
interference nodes which occur when the energy and phase
of the component fluctuations are appropriately matched.
This result shows how the dynamic of the flow driving the
‘‘hydrodynamic’’ part of the nearfield signature generates
sound by a linear process. It furthermore shows that the
nearfield can be considered to comprise a superposition of
convective, ‘‘hydrodynamic’’ and propagative, ‘‘acoustic’’
components.
Progress in data acquisition technology has permitted
progressively larger numbers of microphones to be used
in the nearfield, and this has led to the application of
more sophisticated signal processing techniques. Large
azimuthal nearfield arrays have been used by Ricaud
(2003), Harper-Bourne (2004), Coiffet et al. (2006),
Jordan et al. (2005), Tinney et al. (2006b, 2007), Reba
et al. (2006), Suzuki and Colonius (2006) and Tinney
et al. (2006a). Such measurements have been used to
study the structure of the nearfield in terms of its Fourier-
azimuthal modes: for both single and co-axial subsonic
jets the first 3 Fourier azimuthal modes were found by
Guerin and Michel (2006) and Jordan et al. (2005) to
dominate the near pressure field. Extension of the
microphone distribution in the axial direction has allowed
further information to be obtained regarding the axial
coherence of the Fourier azimuthal modes (Guerin and
Michel 2006; Jordan et al. 2005). In the latter work the
axisymmetric and helical modes were found to have
similarly extensive axial coherence, while for the higher
order modes this coherence is considerably reduced. In the
context of Michalke’s formulation of Lighthill’s aeroa-
coustic theory this suggest that the first two modes will
dominate in the production of sound.
Examples of more ambitious signal processing are typ-
ified by the work of Suzuki and Colonius (2006), who avail
of multiple azimuthal arrays located in the nearfield to
implement a beamforming algorithm for the identification
of instability wave amplitudes; Reba et al. (2006) used
similar nearfield pressure measurements to construct a
wave-packet ansatz for the solution of a boundary value
problem giving the radiated sound field; and Tinney et al.
(2006b) applied a filtering operation in order to separate the
‘‘hydrodynamic’’ and ‘‘acoustic’’ components of the near-
field of heated co-axial jets.
This kind of measurement currently presents a promis-
ing means of studying the role played by the large-scale
coherent flow dynamics in the production of sound. How-
ever, there are a number of difficulties, one of these being
the uncertainty as to the amount of information which is
lost due to the radial distance of the measurement from the
12 Exp Fluids (2008) 44:1–21
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source region. Techniques such as developed by Suzuki
and Colonius (2006) can provide a means of partially
overcoming this difficulty; however, their identification
tool does involve an assumption that the large-scale
dynamics are well-described by linear stability theory. An
attractive means of further reducing this uncertainty is to
perform synchronous measurement of both the near pres-
sure field and the turbulence. This is discussed in the next
section.
3.4 Simultaneous flow/nearfield-pressure
measurements
The mechanisms by which the near irrotational pressure
field is driven by the underlying non-linear rotational flow
dynamics in a subsonic flow are difficult to ascertain
theoretically, for in moving across the short distance
which separates the rotational heart of the flow from its
irrotational near- and mid-fields we pass from a dynamic
in which the pressure field is predominantly elliptic, to
one in which the behaviour is predominantly hyperbolic.
The near pressure field thus constitutes a transition region
where the predominant physics are a strong function of
the radial position. Thus, as mentioned above, interpre-
tation of nearfield pressure measurements is difficult when
a link with the underlying turbulence is sought. By cou-
pling nearfield pressure measurements with velocity
measurements effected in the mixing-layer of the flow
however, some light can be shed on the matter. Laufer
and Yen (1983) show that the fluctuating velocity and
nearfield pressure amplitudes are linearly related over the
first diameter of an acoustically excited jet, while in
Picard (2001) and Picard and Delville (2000) significant
pressure–velocity correlations are demonstrated in an
unexcited jet (M = 0.15, Re = 1.5 · 10–5) using a 16
microphone array and a rake of 12 X-wire probes. Ricaud
(2003) showed similar results at (M = 0.3, Re = 3 · 10–5)
using an 18 microphone axial array synchronously with an
LDV system, as did Tinney et al. (2006b, 2007) at
(M = 0.6, Re = 6 · 10–5) and (M = 0.85, Re = 1 · 10–6)
using azimuthal pressure transducer arrays synchronous
with both LDV and PIV. These studies all show that the
turbulence mechanisms predominant in driving the near-
field pressure are the linear, fast pressures. Tinney et al.
(2006b, 2007) have recently reported correlations between
the nearfield pressure and both the linear and quadratic
mixing-layer velocity terms, and again the predominance
of the linear term is demonstrated; the work of Coiffet
et al. (2006) shows furthermore how sound pressures are
also produced via a linear process, in agreement with
conclusions drawn from the causality methods applied in
the 1970s and 1980s.
3.4.1 Signal processing tools/low order analysis
Progress in measurement technology has led to the use of
progressively larger numbers of microphones, and more
spatiotemporally extensive turbulence measurements via
two-point, three-component LDV and two-point, stereo-
scopic, time-resolved PIV. Such simultaneous sampling of
pressure and velocity can lead to the generation of enor-
mous databases, and in particular when PIV is used to
measure velocity: on account of the temporal limitation of
PIV, large numbers of samples are required in order to
build up the pressure–velocity correlation. Creative post-
processing of the data is thus not simply a possibility, but a
necessity if the huge datasets are to be useful. Tools are
required which can compress the data, both in order to
optimise storage and manipulation, but also from the point
of view of analysis of the underlying physics. It is clear that
some means is necessary by which to make sense of the
thousands of cross-correlations—or other products of syn-
chronous measurement—which can result from such
measurements. Two such means, both based on the second-
order, two-point statistics of a given field or set of fields,
are proper orthogonal decomposition (Lumley 1967) and
linear stochastic estimation (Adrian 1977). From the two-
point statistics of a field quantity (pressure, velocity,
etc…), the flow can be represented in terms of a sum of
empirical eigenmodes, and in many cases a small number
of these suffices to capture the majority of the fluctuation
energy. In such cases a low-order representation of the flow
dynamic is possible. The eigenmodes comprise both spatial
and temporal components. The spatial component trans-
lates some characteristic, spatial flow feature, while the
temporal component dictates how the amplitude of the
spatial component fluctuates in unison with the other
modes in order to reproduce the full flow dynamic. A
particularly attractive feature of POD is that time-resolved
measurements are not necessarily required to obtain the
temporal POD coefficients. This means that time-resolved
flow representations can be obtained from measurements
which are temporally limited. A further attractive feature of
POD is that the temporal POD coefficients represent the
dynamics of a spatially extensive information, which of
course means that its correlation with a time varying
quantity of another measurement will translate a consid-
erably richer information than simple two-point
correlations between two flow quantities [such correlation
leads to what Boree (2003) has described as Extended POD
modes]. As the relationship between the farfield pressure
and its source is governed by a volume integral, this
capacity of POD presents considerable possiblities: some
interesting preliminary results using such an approach have
been obtained by Jordan et al. (2007), who by means of an
acoustically-optimised modal decomposition of a low-
Exp Fluids (2008) 44:1–21 13
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Page 14
Reynolds number jet (computed by Groschel et al. 2005)
were able to make a quantitative estimate of the sound
produced by: a wavy-wall-like mechanism; a more ener-
getic event in the transition region; and by the less-
organised smaller flow-scales.
The second tool which has proved indispensable in
dealing with extensive synchronous pressure–velocity
measurements is linear stochastic estimation (Adrian 1977)
and its improved spectral-based sucessor, as proposed by
Ewing and Citriniti (1997) and later by Tinney et al.
(2006a).5 These techniques are again based on multi-point
correlations between two fields of interest (e.g. nearfield
pressure and velocity), and they lead essentially to the
identification of a transfer function which relates the fields.
Once this transfer function has been identified—and again
for this to be achieved time-resolved measurement of both
fields is not a necessary condition—an extremely valuable
information has been obtained with respect to the physics
underlying the causal link between the two. Indeed, the
transfer function can be used both to understand the
dynamics of one field which were responsible in driving
the other (e.g. the velocity dynamic which was essential in
producing the dynamic of the pressure field in the near and/
or far fields), but also to produce a real-time estimate of
one field using data acquired from the other. Nice examples
of this are the reconstruction of velocity fields using
pressure measurements made in the nearfield (e.g. Picard
and Delville 2000; Ricaud 2003; Coiffet 2006; Tinney et
al. 2006b, 2007).
Natural extensions of these techniques include com-
bined use of LSE and POD (Bonnet et al. 1994), which
involves correlating single point field measurements with
POD coefficients obtained from multi-point measurements
in another field of interest, in order to build a transfer
function which can then be the basis for a subsequent
stochastic estimation. And, finally, a further compression
can be obtained by correlating the temporal coefficients of
POD modes obtained in two fields. Each time it is possible
to correlate two quantities (i.e. whenever a linear rela-
tionship exists), a stochastic estimation is possible.
The capacity of these tools to provide physical insight
which takes us beyond what was possible with simple
point-to-point correlations is considerable, and their future
in the field of aeroacoustics promises to be an exciting one.
Recent examples of where they may be headed can be
found in the work of Picard and Delville (2000), Ricaud
(2003), Coiffet (2006), Tinney et al. (2006b, 2007) and
Jordan et al. (2007). However, there are a number of
important issues, and potential stumbling blocks, which
must be addressed. Take for example the work of Tinney
et al. (2006b, 2007). In this work pressure measurements
taken in the nearfield of a round jet (0.6, 6 · 10–5) are
correlated with velocity signals obtained from LDV mea-
surements in the mixing-layer region. Spectral LSE is then
used to perform a 3D reconstruction of the velocity field
using the near pressure field, whence an aeroacoustic
source term is computed according to Lighthill’s definition.
The source estimate thus obtained, being based on the
mechanisms which were central in driving the near pres-
sure field, corresponds to the low-order, coherent flow
dynamic. However, the Lighthill formulation has been
shown by Freund et al. (2005) to be particularly sensitive
to errors which may arise from such an incomplete repre-
sentation of the source. And so this brings us back to the
question of what constitutes an appropriate source defini-
tion. It is clear that where the experimental approach is
concerned, in addition to questions of what constitutes a
meaningful source definition, a further question arises as to
what constitutes a robust source definition. An interesting
development where this question is concerned is the con-
servative form of the vortex sound theory proposed by
Schram and Hirschberg (2003), who demonstrate how a
reiteration of the momentum and kinetic energy conser-
vation laws leads to a formulation of the vortex sound
theory which is less sensitive to experimental error, and
indeed they used PIV measurements in an acoustically
excited jet to construct a source quantity which leads to
farfield predictions in good agreement with measurements.
As the techniques described above target the low-order,
coherent flow/source dynamic, source definitions derived
from vortex sound theories are probably quite apt, and so
the conservative formulation of Schram and Hirschberg
may constitute a very important tool for such source
analysis and modelling. This constitutes another exciting
prospect for future research: as discussed in Sect. 2.5 there
is considerable redundancy in most source definitions; the
Goldstein framework presents a possibility for the removal,
or at least the reduction of this redundancy; however, this
must not be to the detriment of the robustness of the
resultant source term. These two aspects should be con-
sidered together where experimental source analysis and
modelling is concerned.
4 Contributions from computational aeroacoustics
The advent of high precision direct numerical simulation
(DNS) in the 1990s consituted a major advance for
aeroacoustic research, as it provided a means of exploring
complexities of the sound production mechanisms which
are beyond the reach of current experimental diagnostics. A
comprehensive survey of progress in this specialised
5 The stochastic estimation is in fact exactly equivalent to the
Extended POD, in that the EPOD amounts to the solution of the linear
problem.
14 Exp Fluids (2008) 44:1–21
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branch of aeroacoustics would not be appropriate in this
review paper (the interested reader can refer to papers by
Colonius and Lele (2004) and Wang et al. (2006)), and so
we will simply focus on some of the more pertinent find-
ings where the physics of sound production is concerned
and, in particular where these findings can be compared
with experimental results.
Early simulations were limited to low Reynolds number,
2D flows, entirely dominated by coherent vortex dynamics.
However, this kind of simulation is qualitatively similar to
the excited jet studies undertaken in the 1970s (discussed in
Sect. 3.2.2), and so experimental-numerical comparison is
possible. Mitchell et al. (1995) studied the sound generated
by compact and non-compact co-rotating vortex pairs,
showing the nearfield to comprise quadrupole dilatation
patterns while the farfield was found to be cylindrical: no
inherent directivity was observed. Colonius et al. (1997)
simulated a 2D mixing-layer forced at its most unstable
frequency. This flow is dominated by a vortex pairing
event, and consitutes a spatially stationary, non-compact
source best modelled by a wavepacket structure, but which
produces a strongly directive sound field. We have already
seen how there is a considerable body of evidence sug-
gesting that at least some component of the large-scale
production mechanism in a real jet is spatially stationary,
non-compact and behaves in many ways like a wavy-wall.
These numerical observations lend further support to the
hypothesis that the directive nature of a jet is not related to
convective amplification, but rather to the inherently
directive character of a source structure which is fixed in
space, though generated by moving disturbances, as poin-
ted out by Laufer and Yen (1983). Of course, such 2D, low
Mach number simulations are a long way from the high
Reynolds number jets whose production mechanisms we
seek to understand and model. Freund (2001) was to take
the direct aeroacoustic numerical simulation a step closer
to the real jet by computing a 3D jet (M = 0.9, Re =
3.6 · 10–3). Analysis of the Lighthill source term, and in
particular its radiating structure, revealed two important
features: the regions of radiating source activity did not
correspond to either the peak turbulence levels or the peak
Lighthill source levels, showing very clearly the danger in
interpreting source activity in a flow based on a source
definition which comprises large redundancy; Freund fur-
thermore demonstrated how the radiating source structure
in the low Reynolds number jet resembled a wavy-wall-
like mechanism. This simulation can be compared with: the
low Reynolds number experiments of Stromberg et al.
(1980), where non-linearities associated with wavelike
instabilities were postulated as a possible source mecha-
nism; and the higher Reynolds number flow studied by
Coiffet et al. (2006), in which the existence of a linear
wavy-wall source mechanism was demonstrated. A study
by Sandham et al. (2005) has further demonstrated how
weak non-linearities associated with the linear instability
waves of a 2D mixing-layer produce a sound field very
similar to that computed by DNS, while the sound field
linearly generated by the instability waves was a good deal
weaker; this result can be compared with the experimental
observations of Laufer and Yen (1983) and Stromberg et
al. (1980); however, as we have seen, it may not be an
accurate depiction of the coherent source mechanisms in
high Reynolds number, unexcited flows. Wei and Freund
(2006) used an adjoint based optimisation procedure to
control the flow dynamics of a 2D mixing-layer. This
resulted in reductions of between 5 and 11 dB, depending
on the type of control which was implemented. The neg-
ligible differences observed between the controlled and
uncontrolled flows—despite enormous differences in the
sound power radiated from the flows—is a testament to the
subtlety of the sound producing dynamics of free shear
flows, its closeness to a quiet ‘‘state’’, and the difficulty of
understanding the true ‘‘source’’ structure; a recent study
by Eschricht et al. (2007) has shown how the effect of the
controller involves very slight modifications to the space–
time flow structure, which are sufficient to significantly
degenerate the two-point, two-time source correlations, in
the retarded-time reference-frame. Cabana et al. (2006)
used a DNS of a temporal mixing-layer to understand how
some of the aforesaid redundancies can be removed from a
given source description. A decomposition of the Lighthill
source led to the identification of source mechanisms
associated with the Lamb vector divergence, i.e. the source
term identified by vortex sound theories, and the Laplacian
of the turbulent kinetic energy; the former was found to
dominate sound production in the flow considered. A closer
study of these terms showed how compressibility plays an
essential role in the production of progressive pressure
modes, in agreement with a theoretical description of the
aeroacoustic problem by George et al. (2007). Cabana et
al. (2006) subsequently performed a filtering operation in
wavenumber space (similar to that of Freund 2001) which
led to the identification of the radiating source structure of
the flow.
The simulation of more industrially relevant, high
Reynolds number jets, where the nozzle geometry can be
included, is currently beyond the capability of DNS, and to
this end a powerful surrogate simulation which is becom-
ing increasingly popular is large eddy simulation (hereafter
LES). This kind of simulation uses a coarser space–time
grid, and so only directly computes the larger turbulence
scales, the subgrid scales being either modelled, or ignored
and left to the caprice of numerical dissipation. As the
large-scales appear to play an important role in the pro-
duction of sound however, and as such simulations can
now achieve Reynolds numbers of the same order as flows
Exp Fluids (2008) 44:1–21 15
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of practical interest (e.g. Bogey et al. 2003; Andersson
et al. 2005; Viswanathan et al. 2006), this kind of tool
provides a powerful means for the prediction and study of
jet noise. Some pertinent results which can be compared
with experiment include the causality correlations of
Bogey and Bailly (2005) which again identify the region at
the end of the potential core as an important, intermittent
producer of sound, in agreement with the experiments of
Juve et al. (1980), Guj et al. (2003), Hileman et al. (2005)
and Panda et al. (2005); the two-point space–time corre-
lations of Andersson et al. (2005) were validated by the
experiments of Jordan and Gervais (2005); the co-axial
computations of Viswanathan et al. (2006) identified
important sound sources both at the nozzle exit, and
towards the end of the potential core, both of which were
observed in the experiments of Tinney et al. (2006b) by
means of a nearfield microphone array. Other interesting
results obtained by means of LES include the identification
by Groschel et al. (2005) of the Lamb vector as a dominant
source mechanism in a high Mach number, high Reynolds
number flow, in agreement with the observations of Cabana
et al. (2006); the identification of strong correlations
between entropy and momentum sources by Bodony and
Lele (2006); and the study of the effect of Reynolds
number by Bogey and Bailly (2004).
5 Current candidate source mechanisms
In the foregoing sections we have presented an outline of
the main movements in subsonic jet aeroacoustics over the
past 50 years. We have seen how, in this time, considerable
progress has been made where our understanding of the
mechanisms underlying the production of sound by
unbounded turbulent jets is concerned. And, even if a
general consensus on the matter stubbornly continues to
elude us, there exist nonetheless a number of candidate
source mechanisms, for which a considerable body of
experimental and numerical support can be found.
It seems clear that there are a number of different
mechanisms at work in the production of sound by a jet. In
some respects this is not surprising as a jet presents a
number of well-defined regions, between which the tur-
bulence characteristics vary considerably. The initial
mixing-layer region, just downstream of the nozzle exit, is
characterised by a highly sheared, inflexional mean-flow.
Instabilities in this region of the flow can be rendered more
efficient in the production of sound by the presence of the
nozzle. The experimental results of Bridges and Hussain
(1995) for an excited jet, and Tinney et al. (2006b) for a
high Reynolds, high Mach number co-axial jet, identify an
important source in this region, as do the numerical results
of Viswanathan et al. (2006). The fact that such a strong
source is not observed when the nozzle is not included in
simulations (see for example the results of Bogey and
Bailly 2004) constitutes further evidence for a source
related to the presence of the nozzle.
The region between the nozzle exit and the end of the
potential core has been shown by a number of experimental
studies to be characterised by wavelike instabilities, or
coherent structures (see for example Fuchs 1972; Lau et al.
1972; Chan 1974; Armstrong et al. 1977). Analytical,
experimental and numerical work has shown how such
wavy-wall mechanisms can present spatially stationary,
inherently directive sound sources (see for example the work
of Ffowcs-Williams and Kempton (1978), Laufer and Yen
(1983), Mankbadi and Liu (1984), Crighton and Huerre
(1990) and Colonius et al. (1997)). And, in excited and low
Reynolds number flows, where the flow dynamic is highly
coherent, the sound production mechanism has been argued
to be non-linear (for example Stromberg et al. 1980; Laufer
and Yen 1983; Sandham et al. 2005). However, the exper-
imental observations of Coiffet et al. (2006), and the
numerical results of Jordan et al. (2007) suggest that in
unexcited flows, such instabilities radiate sound via a linear
mechanism. The results of the causality techniques (Lee and
Ribner 1972; Siddon and Rackl 1972; Scharton and White
1972; Seiner 1974; Juve et al. 1980; Schaffar and Hancy
1982) also show the linear component of the Lighthill source
quantity to correlate best with the farfield, in regions both
upstream and downstream of the end of the potential core.
The transition region has long been considered a dom-
inant region where the production of sound is concerned.
The beginning of this region is marked by the annular
mixing-layer at the end of the potential core, where the
wavelike instabilities/coherent structures of the upstream
region undergo a violent transition. Jung et al. (2004)
describe an intermittent ‘‘volcano’’ effect associated with
the collapse of low order azimuthally coherent ring-like
structures. The early causality methods (Lee and Ribner
1972; Siddon and Rackl 1972; Scharton and White 1972;
Seiner 1974; Juve et al. 1980; Schaffar and Hancy 1982)
all identified this region as a dominant source of sound, and
as mentioned, showed the relationship between the turbu-
lent velocity fluctuations and the farfield pressure to be
predominantly linear. Again this contradicts results from
excited flows Laufer and Yen (1983), and indicates that the
source mechanisms in unexcited jets may be fundamentally
different. Events at the end of the potential core have
furthermore been shown to be stationary—and therefore
inherently directive—non-compact, intermittent, powerful
generators of sound (Juve et al. 1980; Guj et al. 2003;
Bogey and Bailly 2004; Hileman et al. 2005; Viswanathan
et al. 2006).
It is important to note that the characteristics of the
source mechanisms described above preclude the use of
16 Exp Fluids (2008) 44:1–21
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statistical modelling approaches involving RANS compu-
tations coupled with an acoustic analogy (cf. Sects. 2.1,
3.1). Even if the non-compactness can be dealt with, the
intermittency cannot, as the RANS computation cannot
provide information regarding the third order velocity
moments. Also, as there can be neither Doppler shift nor
convective amplification associated with a spatially sta-
tionary source, the physical basis of such models must be
seriously questioned. However, in high Reynolds number
flows a further source mechanism may exist related to the
fine-scale, random turbulence. The two similarity spectra
proposed by Tam (1998) and shown to fit subsonic jet noise
data by Viswanathan (2002) support this conjecture, as do
both the acoustically filtered nearfield measurements of
Tinney et al. (2006b), and the differences which have been
identified between high Reynolds number and low Rey-
nolds number flows by Bogey and Bailly (2004) for
example. For this source component statistical models may
be well adapted; however, clarification is first necessary
regarding the associated underlying physics. This presents
a considerable and important challenge for the future.
Analytical decompositions such as performed by Mankbadi
and Liu (1981, 1984), and the recent work of Goldstein
(2005) and Goldstein and Leib (2005) may provide means
by which an integral framework can be obtained for the
experimental/numerical identification and study of this
source component and its relative importance where the
farfield sound is concerned.
6 Concluding remarks
We have tried in the foregoing to give a reasonably com-
prehensive overview of jet noise research since 1952. In
tracing out the various phases which have marked the
evolution of both our understanding of, and the means by
which we endeavour to probe the underlying physics,
something which becomes clear, and, incidentally, which
was evoked by Lighthill (1952) at the outset, is the extre-
mely subtle character of the mechanisms by which a
compressible, turbulent fluid excites a progressive pressure
field. It is on account of this that there remains today a
good deal of controversy and lack of consensus as to what
constitutes a source mechanism in an unbounded shear-
flow. The experimental approach suffers badly at the hands
of this subtlety—the fluctuating levels which characterise
the very-small portion of the jet dynamic implicated in the
production of sound are completely swamped by largely
acoustically ineffective hydrodynamic fluctuations, and are
therefore practically unmeasureable—and is thus obliged
to rely heavily on theoretical frameworks which remain
contentious. Furthermore, and despite our best hopes, even
the recent progress in high-precision numerical simulation
has not been entirely successful in alleviating this apparent
impasse.
There have however been some encouraging recent, and
not-so-recent, theoretical developments, respectively, by
Goldstein (2003, 2005) and Goldstein and Leib (2005), and
by Mankbadi and Liu (1981, 1984). The experimental
approach has become considerably more powerful in its
capacity to access, in a spatiotemporally extensive manner,
the various fields of interest (e.g. Hileman et al. 2005;
Jordan et al. 2005; Suzuki and Colonius 2006; Reba et al.
2006; Tinney et al. 2006b, 2007; Chatellier and Fitzpatrick
2006). And the numerical approach has the capacity to
provide what the experiment cannot (e.g. Freund 2001;
Bogey et al. 2003; Wei and Freund 2006; Cabana et al.
2006). It is clear that what is necessary for the future
development of perspicacious analysis methodologies is a
better synergy between these three disciplines. The theo-
retical frameworks provided by Mankbadi and Liu (1984),
and Goldstein and Leib (2005) warrant further attention,
and most importantly, experimental and numerical analysis
strategies need to be contrived in concert with directives
derived from these theories.
A point which is worth evoking with regard to this is the
following: we seek to identify the space–time signature of
the mechanisms by which the jet couples with the farfield.
This signature is contained in the farfield. In fact, this
signature is the farfield. And while it is well known that it
is not possible to obtain a unique solution for source dis-
tributions from farfield information alone (by inverse
techniques for example), coupled sampling of farfield
pressure with extensive flow data can lead to an improved
conditioning of such inversion techniques. The causality
methods used in the 1970s constituted an early attempt at
such identification (Lee and Ribner 1972; Siddon and
Rackl 1972; Scharton and White 1972; Seiner 1974; Juve
et al. 1980; Schaffar and Hancy 1982), and both Guj et al.
(2003) and Hileman et al. (2005) have more recently made
similar good use of such nearfield–farfield coupling.
However, we now have the capacity, both in terms of
measurement technology and signal-processing, to take
these approaches much farther. In addition, numerical
simulations are well situated to help understand the limits
of such techniques. The simulation can be used to help
optimise the experiment. The adjoint-based approaches
which are now beginning to be applied numerically (Wei
and Freund 2006) constitute an upper limit in terms of
what’s possible, and these need to be exploited to help
understand how much can be achieved experimentally.
Ambitious research programmes are required which com-
prise three indispenable phases: a first in which a thorough
theoretical treatment and definition of the problem is
considered; a second phase involving a numerical investi-
gation which pushes the theory to its limits; and a third
Exp Fluids (2008) 44:1–21 17
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experimental phase which is optimised by virtue of lessons
learned during the numerical phase. High-powered signal
processing will be central to effective mining of the
numerical and experimental databases, and in this regard
an integration of techniques from other research fields
should be encouraged. In particular, research fields where
pattern-recognition and structure-identification are central
could constitute a source of new ideas: fields where tech-
niques are developed in order to understand the
relationship between different kinds of N-dimensional
signature, and whose extrapolation to the field of jet
aeroacoustics could help answer the question: what was the
space–time flow pattern which generated this signal (the
farfield)? Such an approach is currently being developed by
Jordan et al. (2007).
It seems clear that, despite some formidable obstacles
the future of aeroacoustic is set to be an exciting one,
where genuinely new analysis strategies can be made
possible by an efficient synergy between theoretical,
experimental and numerical disciplines, one which takes
good advantage of the impressive recent progress in
numerical and experimental tools; however, we would like
to close this paper by suggesting that there is a further
essential element, and this is: a keen sense of adventure!
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