On the vertical structure of the tropospheric eddy momentum flux Farid Ait Chaalal (1,3) and Tapio Schneider (2,3) (1) Brown University, Providence, USA (2) ETH, Zurich, Switzerland (3) Caltech, Pasadena, USA 19th Conference on Atmospheric and Oceanic Fluid Dynamics 17–21 June 2013, Newport, Rhode Island
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On the vertical structure of the tropospheric eddy momentum flux
Farid Ait Chaalal(1,3) and Tapio Schneider(2,3)(1)Brown University, Providence, USA (2)ETH, Zurich, Switzerland
(3)Caltech, Pasadena, USA
19th Conference on Atmospheric and Oceanic Fluid Dynamics17–21 June 2013, Newport, Rhode Island
Eddy momentum flux maximum in the upper troposphere
Held, 2000: upper level zonal mean flow favors linear wave meridional propagation
Upper level enhancement not captured without nonlinear saturation (Simmons and Hoskins, 1978; Merlis and Schneider, 2009)
10�6ms�2
Motivation
Eddy momentum flux convergence in the atmosphere (colors), zonal wind (contours, m/s) andtropopause (grey line).ERA 40 1980-2001
Latitude
Sigm
a
10
10
3030−10
−60 −30 0 30 60
0.2
0.8
−50
0
50
10
2020
0
0
Surface friction?
Large scale eddy-eddy interactions?
Outline
Why is eddy momentum flux concentrated in the upper troposphere?
An idealized dry GCM
GFDL pseudospectral dynamical core
Radiation: Newtonian relaxation toward temperature profile
Convection: relaxation of vertical lapse rate toward 0.7 ⨉ (dry adiabatic)
Uniform surface, no seasonal cycle
Run at T85 with 30 vertical sigma-levels
600 days average after 1400 days spin-up
(Schneider and Walker, 2006)
The role of surface friction
Colors: eddy momentum flux divergenceContours and dashed lines: zonal mean flow (m/s)Dotted line: potential temperature (K)Grey line: tropopause (2K/km lapse rate)
Simulation with positive 90 K pole-to-equator temperature contrast ∆h.
Simulation with negative ∆h = -90 K.Poles heated, tropics cooled.
10�6ms�2
LatitudeSigm
a
−10
−20
−30−40 −40
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
10
Latitude
Sigm
a
30 30
10
10
20 20
300
320
350
−60 −30 0 30 60
0.2
0.8
−50
0
5010�6ms�2
Removal of eddy-eddy interactions
Quasi-linear (QL) model (O’Gorman and Schneider, 2007)
Retained:Wave-mean flow interaction (mean flow = zonal average)Interaction of waves of opposite zonal wavenumber
(Reynolds stress)
Neglected:All other eddy-eddy interactions
(Statistics equivalent to 2nd order cumulant expansion, see Brad Marston’s talk)
Full
No eddy-eddy
Meridonal circulation
Contours: zonal mean flow (m/s)
Dotted lines: potential temperature (K)
Grey line: tropopause
Latitude
Sigma
30 30
2020
10 10
300
320
350
−60 −30 0 30 60
0.2
0.8
Eddy Momentum Flux Divergence
Latitude
Sigm
a30 30
10
10
20 20
300
320
350
−60 −30 0 30 60
0.2
0.8
−50
0
50
Colors: eddy momentum flux convergence
Contours: zonal mean flow (m/s)
Dotted lines: potential temperature (K)
Grey line: tropopause
Eddy momentum flux convergence
Full
No eddy-eddy
10�6ms�2
Restoring barotropic triads
Latitude
Sigm
a
10 10
1010
40 40
300
320
350
−60 −30 0 30 60
0.2
0.8
−50
0
50
Latitude
Sigm
a30 30
10
10
20 20
300
320
350
−60 −30 0 30 60
0.2
0.8
−50
0
50
10�6ms�2Colors: eddy momentum flux convergence
Contours: zonal mean flow (m/s)
Dotted lines: potential temperature (K)
Grey line: tropopause
Full
Withbarotropic
triads
Baroclinic wave lifecycle experiments
Initialize a zonal wavenumber 6 perturbation in the zonally averaged circulation (fully non-linear model)
Experiments run with full model, no eddy-eddy model, and model with only barotropic triads
Why eddy momentum flux not maximum in the upper troposphere in the QL model ?
Why enhancement captured when barotropic triads are restored?
Also: eddy kinetic energy larger in the QL model usually, larger momentum flux expected
Removal of eddy-eddy interactions
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75−5
0
5
10
x 10−5 full model
Days
W/kg
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75−5
0
5
10
x 10−5
Days
W/kg
only barotropic eddy−eddy
0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75−5
0
5
10
x 10−5
Days
W/kg
no eddy−eddy
Baroclinic conversion.Eddy available potential energy to eddy kinetic energy
Barotropic conversion.Zonal kinetic energy to eddy kinetic energy
Colors: Eddy momentum fluxes ()Dashed lines: winds in m/sDotted line: potential temperature in KGrey line: tropopause
Friction/10 Friction Friction * 10
The role of surface friction
Colors: Eddy momentum fluxes divergenceDashed lines: winds in m/sDotted line: potential temperature in KGrey line: tropopause
Simulation with positive ∆h = 90 K Surface friction balances upper level momentum fluxes divergence (EMFD)
Long been recogn i zed e f fec t on midlatitudes eddies amplitude, jet streams strength and location, energy conversions (James, 1987; Robinson 1997; Chen et al., 2007; etc...)
Can it explain upper level EMDF e n h a n c e m e n t ? S o m e t i m e suggested in text books (e.g. Vallis, 2006)Latitude