Post on 25-Jul-2015
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
Full
No eddy-eddy Only barotropic eddy-eddy
Energy conversion
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
DaysW/kg
no 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 full model
Days
W/kgColors: QG potential vorticity fluxContours: zonal mean flow (m/s)Arrows: QG Eliassen-Palm vector
Full No eddy-eddy Only barotropic eddy-eddy
10�5ms�2
Latitude Latitude Latitude
Sig
ma
Maximum of barotropic conversion
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
DaysW/kg
no 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 full model
Days
W/kg
Sig
ma
Latitude Latitude Latitude
Minimum of baroclinic conversion
Colors: QG potential vorticity fluxContours: zonal mean flow (m/s)Arrows: QG Elliassen-Palm vector
Full No eddy-eddy Only barotropic eddy-eddy
10�5ms�2
Potential vorticity rearrangement and mixing
Days
W/kg
15 20 25 30 35−5
0
5
10x 10
Days
W/kg
15 20 25 30 35−5
0
5
10x 10
For a theoretical study of critical layers (SWW solution) in the QL approximation:Haynes and McIntyre, 1987
Full(350 K
isentrope)
No eddy-eddy
(320 K isentrope)
Day 26 Day 30 Day 35
Day 17 Day 22 Day 30
PV fields on isentropes
210PVU
Potential vorticity rearrangement and mixing
Days
W/kg
15 20 25 30 35−5
0
5
10x 10
15 20 25 30 35−5
0
5
10
x 10−5
Days
W/kg
only barotropic eddy−eddy
Noeddy-eddy
(320 K isentrope)
Only barotropic eddy-eddy
(320 K isentrope)
Day 17 Day 22 Day 30
Day 25 Day 28 Day 32
PV fields on isentropes
210PVU
Conclusions
Surface friction not an important factor
Wave packets generated in LT propagate upward until they reach UT and tropopause, where horizontal propagation is favored
Vorticity rearragement and mixing through eddy-eddy interaction near critical layers essential
Keeping only barotropic triads captures the enhancement
Understanding nonlinear barotropic critical layer dynamics might suffice
Why is eddy momentum flux concentrated in the upper troposphere?
Conclusions
What still favors meridional propagation of waves in the upper-troposphere? (tropopause as a wave guide? ...)
Index of refraction for zonal wavenumber 6 baroclinic waves.
Latitude
Sigm
a
30 30
1010
−60 −30 0 30 60
0.2
0.8
0
5
10
15
20
Why is eddy momentum flux concentrated in the upper troposphere?
FullNo
eddy-eddy
Dry GCM without eddy-eddy interactions
Removal of the eddy-eddy interactions (O’Gorman and Schneider,2007).Advection of a quantity a = a + a0 by the meridional flow v = v + v 0
(zonal mean/eddy decomposition):
@a
@t= �v
@a
@y= �v
@a
@y� v
@a0
@y� v 0 @a
@y� v 0 @a0
@y
transformed into
@a
@t= �v
@a
@y� v
@a0
@y� v 0 @a
@y� v
0 @a
0
@y
Statistics of such a model are equivalent to a second order cumulantexpansion (third order cumulants set to 0 in the second orderequations).
Farid Ait-Chaalal (Caltech) Second-Order Atm. Circulation June 26, 2012 4 / 19
@a
@t= �v
@a
@y= �v
@a
@y� v
@a0
@y� v0
@a
@y� v0
@a0
@y
@a
@t= �v
@a
@y= �v
@a
@y� v
@a0
@y� v0
@a
@y� v0
@a0
@y
Removal of the eddy-eddy interactions
Latitude
Sigm
a
0 0
−5
−10
−30
−40 −40
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
10
The role of surface friction
Latitude
Sigm
a0
0
−5
−10
−30
−40 −40
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
10
Simulation with ∆h = -90 K
Latitude
Sigm
a
10
5
10
5 −50 −50
−40−30
−10
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
10
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
Sigm
a
30
10
−5 −5
−10
300
320
350
−60 −30 0 30 60
0.2
0.8
−10
−5
0
5
105.10�6ms�2