Atmospheric waves from the point of view of a modeler

Alexander Medvedev

2

Wave-mean flow interactions

2

)','(),()(

'

),()(

YYNQYYNYL

YYY

QYYNYL

Atmospheric dynamics is described by the non-linear equations:

forcing.eddy theis )','( eddies, theare ' flow,mean theis YYNYY

3

Meridional circulation

3

yzzyt uvuwvfuwuvu )''()''(1

xt fvuu v

PWGW

Detailed knowledge of the wave field is not needed. Only averaged quantities (fluxes)

Meridional circulation is determined by eddy forcing, at least away from low latitudes, where f is small

4

Meridional circulation

4

The bold ellipse denotes the thermally-driven Hadley circulation of the troposphere. The shaded regions (“S”, “P”, and “G”) denote regions of breaking waves (synoptic-, planetary-scale waves, and gravity waves), responsible for driving branches of the strato- and mesospheric circulation.

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“Gyroscopic pump” in action

CRISTA measurements of NO2 [JGR,2002,107(23)]. p=30 mbar, z ~30 km

Eddy-driven circulation on Earth and Mars

66

MAOAM Mars GCM

7

Mean zonal circulation

yzyzyt vvwufauvwvvv )cos'()''(tan 2112

Cyclostrophic wind

• Eddies modify zonal wind a) indirectly (through pressure/temperature field),and b) directly (eddy forcing)• On Earth eddy forcing is weak, and the wind is thermal (cyclostrophic).• On Mars, it appears that eddy forcing is significant in the MLT.• On Venus?• GCM is the ultimate tool to figure this out

The Hide theorem: superrotation cannot develop in a purely axisymmetric flow

8

Gravity wave forcing

8

9

Evolution of the GW momentum flux

9

''''

wudz

wuddissbreak

z

')(exp)()()(''''

0

100 dzzzzwuwu diss

z

z

break

''wuonAccelerati

“Universal” spectrum on Earth: kh ~ k -5/3

Long waves produce less drag. But there are more of them.Short waves produce more drag. But there are less of them.Main portion of the drag is produced by harmonics with ~ 100-500 km.

k

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GW parameterization problem

tmkmzkxiTvuTvu ),(exp),,('...),','(

uk

Nk

uc

Nm

Amplitudes of momentum fluxes at a reference level + any pair of these two eigenvalues fully define the problem of GW parameterization

Alternatively, amlitudes … can be used

22 ',' Tu

11

Filtering and momentum deposition

11

The sign of acceleration depends on the sign of GW momentum fluxes,or intrinsic phase velocity, )( uc

2')(~'' uucwuonAccelerati

Diurnal variations of GW drag

12

Effect of GWs is not always to decelerate the flow

Yigit and Medvedev, 2010

13

GW breaking

Billows due to shear instability

“Streaks” perpendicular to the incident IGW and having smaller scales: wave breaking

More breaking?

14

GW interference

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1616

GW on Mars

• Generation of GWs on Mars is likely much stronger

• This implies larger GW amplitudes (~2 – 5x), momentum fluxes (~10x)

• However, GCMs are apparently able to reproduce the circulation (up to 80-100 km) without GWs

• What is the dynamical importance of GWs?

• Previous simulations - were limited by 80-100 km - parameterizations considered only terrain-generated

harmonics (c=0)

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GW activity between 10-30 km

MGS radio occultation temperature

Orographic wind stress

GW potential energy, short waves

Creasey, Forbes, Hinson, GRL, 2006

u’ 2=2Ep |u’| ~ 1.4 to 4 m/s

1818

Spectral GW drag scheme

GW fluxes at the source level (~8 km)

Extremely important above the turbopause

Hertzog et al., JAS, 2008

Yigit, et al., JGR, 2008, 2009; Yigit and Medvedev, GRL, 2009; JGR, 2010

1919

Estimates with the MCD

Medvedev, Yigit and Hartogh, Icarus, 2011

2020

Zonal wind and drag, solstice

2121

Meridional wind and drag, solstice

2222

Temperature, solstice

Summary

What modelers need to know?

•Statistics of momentum fluxes, or wave amplitudes, or whatever correlations possible

•Spectral statistics: wavelengths, frequencies, phase velocities, propagation azimuths

•A clue about where the sources are located

•An indication where GWs break, if at all

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Waves are everywhere!

Picture taken from the Institute’s roof