General Circula,on of the Atmosphere

Transcription

1 General Circula,on of the Atmosphere Today: Angular momentum transport - how do eddies affect the mean flow? Eulerian view Transformed Eulerian Mean EP fluxes Momentum budget Local momentum fluxes: E vectors 1

2 Westerly momentum carried poleward Easterly momentum (weakened by fricgon) carried equatorward

3 Eddy shape is crucial for angular momentum transport No momentum transport Momentum converged into jet Reality is generally asymmetric long trailing troughs drag momentum from subtropics. Aim: derive expressions for the change in the mean flow due to the eddies.

4 Start with zonally averaged QG system: drag diabagc heagng Where the buoyancy is

5 Steady state balances are: Coriolis balances eddy momentum flux Ascent and adiabagc cooling balances eddy heat flux and diabagc heagng

6 Apply thermal wind balance and sub in this for u and b from below gives where z y

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8 Holton (1992) Heat fluxes lead to thermally indirect circulagon in mid- lats

9 Holton (1992) Momentum fluxes lead to thermally indirect circulagon in mid- lats

10 What s the problem? Eddy terms in both u and b eqns, yet these are coupled by TWB Strong cancellagon between eddy and mean flow terms, especially eddy heat flux and adiabagc cooling SoluGon: Transformed Eulerian Mean (Andrews & McIntyre 1976) Define residual circulagon to remove the above cancellagon: where

11 What do we learn? Eddy heat and momentum fluxes don t act separately. EP flux measures the total effect of the eddies on the zonal mean wind (even if waves aren t well described by linear theory. Can show that the divergence of the EP flux equals the poleward eddy (QG) PV flux And conversely the zonal mean PV is determined by the EP fluxes We can also derive a conservagon law for the wave acgvity density so the EP flux is a flux of wave acgvity.

12 Easterly acceleragon Westerly acceleragon Eddy driving acts to barotropise the westerlies, giving deep eddy- drvien jet

13 Residual mean vergcal circulagon is proporgonal to the diabagc heagng. EffecGvely the diabagc circulagon: Eg. Parcels that rise are diabagcally heated to adjust to the local environment. Hence approximates the mean mogon of air parcels. Note: This is all heagng, not just transient

14 LC1 Day 0: low level b fluxes dominate Day 5: b fluxes have deepened, waves propagagng up Day 8: upper level momentum fluxes as waves propagate eq ward Time mean similar to obs climate

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16 Transient StaGonary StaGonary fluxes similar to transient but weaker Summer likely not well sampled here

17 Example: Zonal wind regressed on SAM Divergence: AcceleraGon of u Convergence: DeceleraGon of u Poleward shie of baroclinic eddy generagon Lorenz and Hartmann (2001)

18 Angular momentum budget Atmosphere gains from Earth in tropics due to drag on easterlies Atmosphere loses to Earth in extratropics due to drag on westerlies Poleward transport accomplished by eddies

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20 Angular momentum budget Holton chapter 10 Define absolute angular momentum: Can then derive the budget for a zonal ring of air of unit meridional width extending over the depth of the atmosphere (in sigma coordinates). Convergence of meridional ang. mom. flux Small scale turbulent fluxes at surface Surface pressure torque Tend to have higher pressure on western side of orography, ie providing drag on the atmosphere almost half of the surface fluxes in mid- lagtudes. High p Atm pushes Earth Earth pushes atm Low p

21 Tropics: Westerlies at upper levels stronger than surface easterlies. So Hadley cell transports angular momentum poleward. Extratropics: Here the angular momentum flux is dominated by the transient term, and hence proporgonal to the negagve of the meridional EP flux.

22 E Vectors ~ lat- long wave ac,vity flux. Like EP fluxes but based on deviagons from the Gme mean, rather than the zonal mean E = ( ) 2 2 v' u' u' v' Divergence : Accelerates westerlies Convergence : Decelerates westerlies Hoskins et al 83

23 3D formulagon includes vergcal component comprising the eddy heat fluxes Hoskins et al (1983)

24 High- pass E along with u at 250mb for one winter

25 High- pass E in 3D using v T at 700mb for the same winter