Download - Aofd farid

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




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




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


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


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


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


Noeddy-eddy

(320 K isentrope)

Only barotropic eddy-eddy

(320 K isentrope)



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


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


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


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


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

Download - Aofd farid

Top Related