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TURBULENT MIXING OF CLOUD WITH THE ENVIRONMENT:TWO-PHASE
EVAPORATING FLOW AS SEEN BY PARTICLE IMAGING VELOCIMETRY
Szymon P. Malinowski1 Piotr Korczyk2, Tomasz A.
Kowalewski21Institute of Geophysics, University of Warsaw,
Poland
2Institute of Fundamental Technological Research, Polish Academy
of Sciences, Warsaw, Poland.
1. INTRODUCTIONWe present new experimental results that
demonstrate influence of evaporative cooling and buoyancy
fluctuations on the anisotropy of small-scale turbulence in clouds
(c.f. (Andrejczuk et al.,2004), (Andrejczuk et al., 2006), (Korczyk
et al.,2006), (Malinowski et al., 2008)). In these papers results
of the numerical and laboratory experiments with small-scale
turbulent mixing of cloud with unsaturated environmental air are
discussed. The key findings indicate importance of small-scale
fluctuations of buoyancy. These fluctuations are caused by
evaporation of droplets mixing and from droplet sedimentation.
Effecting buoyancy forces influence small-scale turbulence in
clouds, making it anisotropic and more vigorous than expected.
The set-up of the experiments described here is designed to
mimic basic aspects of small-scale turbulent mixing of a cloudy air
with unsaturated environment. Thermodynamic conditions
reconstructed in the chamber are, however, slightly different from
those typical for clouds due to requirements of the visualization
technique. Nevertheless, we believe that documented small-scale
anisotropy of turbulent motions calls for the experiment
investigating its role in natural conditions.
2. EXPERIMENTAL SETUPThe experimental setup is based on
experiences
gathered in earlier attempts (Malinowski et al.,1998),
(Jaczewski and Malinowski 2005), (Korczyket al., 2006). In the
laboratory mixing takes place inside a cloud chamber of dimensions
of 1.0 m ×1.0 m×1.8 m, (Figs 1 and 2 , for the detailed description
consult (Korczyk et al., 2006) and (Korczyk 2008)).
Saturated and negatively buoyant cloudy plume (containing
droplets of ~10 μm diameter) enters the chamber through the round
opening in the ceiling. The initial velocity of the plume is about
20cm/s at the inlet, and it increases to about 30 cm/s in the
middle of the chamber in response to the buoyancy forces. LWC in
the plume is typically more than 10 g/kg --- somewhat higher than
in natural clouds. The plume's temperature is about 25oC, close to
the
temperature of the unsaturated chamber air. Relative humidity of
the clear air inside the chamber varies from 20% to 65% for
different experiments. The plume descends through the chamber while
mixing with the environment, creating complicated continuously
evolving structures (eddies, filaments, etc.).
Fig.1 Cloud chamber with the laser producing planar sheet of
light and CCD cameras.
Fig.2. The principle of the visualization technique. A pulsed
laser with the suitable optical system produces planar sheet of
light. Light scattered by cloud droplets is imaged with the CCD
camera.Droplet spectra at the inlet to the cloud chamber have been
measured by a microscopic technique: droplets were collected on a
glass plate covered with the silicone oil and imaged with the
microscope. The data were processed with the algorithm allowing for
determination of droplet diameters. Results, presented in Fig. 3
indicate that initial droplet spectrum is not atypical for natural
clouds.
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Fig.3 Initial droplet spectrum. Vertical axis: relative mass,
horizontal axis – droplet radius [μm]
Illuminating the chamber interior with 1.2 mm thick sheet of
laser light enables imaging in a planar cross section through the
scene with a high-resolution CCD camera. An example image from the
experiment, covering an area of 9×6 cm2, is presented in Fig 4.
Fig 4: The negative of the image from the experimental chamber
showing small-scale structures created in a process of cloud-clear
air mixing. Imaged area corresponds to 9×6 cm2 in physical
space.
The image reveals fine structures created in the process of
turbulent mixing of the cloud with its unsaturated environment. One
pixel corresponds to 1.2 mm deep volume with about 69×69 μm2 area
in the plane of the laser-light sheet. Such elementary volumes
occupied by droplets are represented by dark pixels; bright pixels
correspond to volumes void of droplets.
Pattern recognition in two consecutive images separated by a
known time interval allows to retrieve two velocity components in
the image plane. This technique, referred to as Particle Image
Velocimetry (PIV) (Raffel 1998), is widely adopted in experimental
fluid mechanics. An original, accurate multi-scale PIV algorithm
was developed for this experiment (Korczyk et al., 2006), (Korczyk
2008).
First, it identifies motions of large structures, and then
analyzes the displacements within the structures. Application of
the algorithm allows estimating the two components of velocity
vector with spatial resolution of about 0.07 mm; i.e., an order of
magnitude smaller than the Kolmogorov length scale, the value of
which was estimated from the measurements at approximately 0.76 mm.
Fig. 5 shows an example pattern of droplets superimposed on the
retrieved velocity vectors.
Fig. 5. Two components of velocity field retrieved by means of
PIV technique. 3. RESULTS
The data were collected in a series consisting of 50
experiments, each subject to slightly different thermodynamic
conditions inside the chamber. For each experiment, at least 100
pairs of frames (tens of thousands of velocity vectors in each
frame) were analyzed, in order to retrieve statistical properties
of velocity fluctuations.
3.1. Anisotropy of turbulent velocity fluctuationsExperimental
probability distribution functions
(PDF) of the velocity fluctuations in horizontal (u') and
vertical (w') directions are summarized in Table 1. It follows,
that PDF of w' is wider than the PDF of u'. The derived kurtosis
and skewness indicate that both distributions are close to
Gaussian. The ratio of velocity variances =0.46±0.07 (a mean over
all 50 experiments) is consistent with the numerical simulations,
discussed in (Malinowski et al., 2008). Mean Taylor microscales,
estimated independently for horizontal (λ1) and vertical (λ3)
velocity components, are 7.5±0.4 mm and 9.2±0.6 mm, respectively.
These values, obtained from measurements resolving smallest scales
of the flow, also indicate anisotropy in agreement with results of
numerical simulations ((Malinowski et al., 2008) and references
therein).
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Table 1. Distribution of horizontal (u') and vertical (w')
turbulent velocity fluctuations. Average from 50 experiments.
Standard deviation [cm/s]
Skewness Kurtosis
u' 5.4 -0.01 3.2
w' 8.0 -0.2 3.1
Fig.6 Longitudinal (upper panel) and transversal (lower panel)
2nd order structure functions of horizontal (red) and vertical
(green, dashed) turbulent velocity fluctuations evaluated from PIV
measurements 70 cm from the inlet to the cloud chamber.
More on anisotropy can be inferred from presented in Fig. 6
structure functions of turbulent velocity fluctuations calculated
according to the formulas:
Here superscripts II and ┴ denote longitudinal and transversal
directions, respectively; u and w are horizontal and vertical
turbulent velocity fluctuations in the plane of the image; x and z
are horizontal and vertical coordinates in the image; means
averaging over many scenes. We see a considerable differences
between the structures
along and across the flow. In the whole range of scales
investigated the most variable are the horizontal differences of
the vertical velocity.
3.2. Effects of evaporative cooling and liquid phase load.
Anisotropy of small-scale turbulence in the laboratory
experiments is most likely the result of evaporative cooling at the
cloud-clear air interface, but the impact of the other buoyancy
effects cannot be ruled out. This is corroborated by additional
experiments using the same laboratory setup but with
non-evaporating oil (DEHS) droplets replacing cloud water (Korczyk
2008) of spectrum presented Fig. 7. The observed ratio in these
experiments was 0.86±0.02, suggesting non-negligible impact of the
buoyancy oscillations, due to weight of oil droplets in “oil cloud”
filaments, on the observed small-scale anisotropy.
Fig.7 Spectrum of DEHS droplets. Vertical axis: relative mass,
horizontal axis – droplet radius.
In order to analyze the role of evaporative cooling of water
droplets at the cloud-clear air interface on the buoyancy
fluctuations consider mixing diagrams of cloudy air entering the
chamber with the clear air of various relative humidities (RH, Fig.
8).
Fig. 8. Mixing diagrams (vertical axis: density temperature,
horizontal axis – mixing proportion of cloudy air) for conditions
in the cloud chamber.
The TKE dissipation rate ε is estimated with use of PIV
measurements from the relation:
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;
where ν is kinematic viscosity of the air.The amplitude between
the maximum and the
minimum density temperature at given RH of the environmental air
indicates the potential for buoyancy oscillations due to both
effects: evaporative cooling and liquid water load. It follows,
that for the conditions in the chamber the maximum buoyancy
fluctuations are at low relative humidities, at which evaporative
cooling (at high liquid water loads in the chamber) is most
efficient. In such a case a systematic relation between the
relative humidity (in the range 20%-50% at which potential for
buoyancy fluctuations changes) and some parameters of turbulence
should be measurable. Fig. 9 documents such systematic relation.
The dependence of the TKE dissipation rate on the relative humidity
of the environmental air is evident.
Another result documenting effect of evaporative cooling on the
intensity of the small-scale turbulence is shown in Fig. 10. It
presents 2nd order structure function of horizontal velocity
fluctuations for experiments with different relative humidities of
the environmental air. At low RH, at which contribution of
evaporative cooling to buoyancy fluctuations has its maximum,
structure function indicates large velocity differences. These
differences decrease with increasing RH.
CONCLUSIONSResults presented here confirm that small scale
buoyancy fluctuations cause anisotropy of small scale
turbulence. Two effects which contribute to these fluctuations are
identified: evaporative cooling and uneven spatial distribution of
droplets in cloud and clear air filaments (uneven distribution of
liquid phase load).
Effect of evaporative cooling depends on the thermodynamical
properties of cloud and clear air. Mixing diagram of shows the
possible range of buoyancy fluctuations due to evaporative cooling.
Increased range of buoyancy fluctuations results in more intense
turbulence.
Effect of mass load, documented in experiments with non
evaporating droplets, requires more investigations.
Third effect, additional transport of liquid water due to
sedimentation of droplets (Andrejczuk et al.,2006) may contribute
to first two: evaporative cooling and mass load. All effects
combined cause, that small-scale turbulence in non-uniform cloud is
anisotropic with the privileged direction in vertical.
Fig.9 Dependence of the relative humidity (horizontal axis) in
the cloud chamber on the TKE dissipation rate estimated from PIV
measurements. Consecutive plots show results of measurements at
50cm, 60cm and 70cm from the inlet to the cloud chamber.
Fig. 10. Longitudinal 2nd order structure function of u for
varying relative humidities of the environmental air, measured 30
cm from the inletReferences:Andrejczuk, M., W.W. Grabowski, S.P.
Malinowski and P.K.
Smolarkiewicz, 2004: Numerical simulation of cloud-clear air
interfacial mixing. J. Atmos. Sci., 61, 1726-1739.
Andrejczuk, M., W.W. Grabowski, S.P. Malinowski and P.K.
Smolarkiewicz, 2006: Numerical Simulation of Cloud-Clear Air
Interfacial Mixing: Effects on cloud- microphysics. J. Atmos. Sci.,
63, 3204-3225.
Korczyk, P.M., S.P. Malinowski and T.A. Kowalewski,2006: Mixing
of cloud and clear air in centimeter scales observed in laboratory
by means of particle image velocimetry. Atmos. Res., 82,
173-182.
Korczyk. P., 2008: Effect of cloud water on small-scale
turbulence - laboratory model (in Polish), PhD thesis, IPPT, Polish
Academy of Sciences.
Jaczewski. A. and S.P. Malinowski, 2005: Spatial distribution of
cloud droplets investigated in a turbulent cloud chamber. Q. J.
Roy. Meteorol. Soc,. 131, 2047-2062.
Malinowski. S.P., M. Andrejczuk, W.W. Grabowski, P.K. Korczyk,
T.A. Kowalewski and P.K. Smolarkiewicz,2008: Laboratory and
modeling studies of cloud-clear air interfacial mixing: anisotropy
of small-scale turbulence due to evaporative cooling. New J. of
Physics, accepted..
Malinowski, S.P., I. Zawadzki and P. Banat, 1998: Laboratory
observations of cloud-clear air mixing in small scales. J. Atmos.
Oceanic. Technol., 15, 1060-1065.
Raffel, M., Ch.E. Willert and J. Kompenhans, 1998: Particle
image velocimetry: a practical guide. Springer.
1. INTRODUCTION2. EXPERIMENTAL SETUP3. RESULTS3.1. Anisotropy of
turbulent velocity fluctuations3.2. Effects of evaporative cooling
and liquid phase load.
CONCLUSIONS