forces Coriolis f. deviation to the RHS in q high - PDF document

Applied Talks PhD @ HW Surface Semi Equations geo strophic - Lisei Stefania 02/05/18 of naturally Geophysical Fluid fluid dynamics Dynamics : flows Occur ing atmosphere such a as oceans , Dynamics dominated by : Rotation Pressure gradient ⑤← forces Coriolis f. µ deviation to the RHS in q high pressure / sine f=2R N . atmosphere horizontal gradient . pressure o along f- equator ⇒

behave force Geographic Coriolis deviates pressure : gradient It dynamics isobars by along so , friction Limitation ! : Friction Coriolis force weakens gn ⑤ high pr% before 0 cyclones a 0 ① anticyclones We model for need & with better atmosphere a oceans balance approximation than apostrophe : - apostrophe ( QG ) equations but less quasi easier precise - : , I fully - goo strophic SG ) I semi equations complex more : - nonlinear ) for dynamics but better approximation some formation ) fronts I eg .

I incompressible equations Semi goo strophic ) in viscid : - , . D) I ft igtffuz fu ) at the to 0 = = Ig off Ia t fzp I = t ages strophic → ✓ the strophic wind full div I velocity wind 0 = f- dyp , 2×10 ) fig = pressure f= buoyancy anomaly to = , I ft . D) t the f Coriolis frequency constant o assumed = = , Ig balance the solution the gene strophic is in . : Rossby number Ro Important quantity . effect Ro how the of Earth rotation for the strong measures is = ¥ dimensionless ) dynamics I Ro . . Ro behave friction I to apostrophe I 0 corresponds = no QG physical meaning have when Ro SQ a small is .

Some references : Eliasson into ' SG 48 - : . ' 72 Hoskins useful for A Bretherton large-scale SG is - : dynamics front a genesis - Hoskins ' 75 intro SSG and apostrophe coordinates : . ' 84 Cullen results A Purser Lagrangian on space - : . : stability principle Cullen Shuts 9 I 87 - - Cullen ' 06 book scale atmospheric flows henge loonie on : . Benemou ' 98 of Brenier week solutions apostrophe A SG in - : Optimal Transport coordinates through . De Philipp is , Colombo Ambrosio , Figolli ' week solutions ' 12 16 - : , , domains special on . Bad A Regine SSG 46 in numeric on - : .

Surface Gees trophic semi Equations - ' 75 ) Hoskins I IR2 x intro tnensf lol ) word D= on 3151 III. think that ) = for Use X= IX. 42 ) coordinates guest . A def stream function I X sit new is on . DX IH1H IHIIXI 't ) Dap = for E. → new eg Assuming b. constant PV t as 0/0=0 ftttw IR2 ¥ on . Issa THIN Given formally TITI if 4--5/2=1 define f. 4 and = DE ' l2xy$ ) 2xx$2yy§ = - am

Need define T to rigorously . Thm I ' 18 ) Wilkinson L There Go exists constant st given . a , . " CITY EE0Y EC solution of there -0 smell exists a , Moreover IBVP ) small ball § is unique on a . . , of proof Idea BFPT elliptic theory for the linear BVP t : It d. TTY It Thm , Wilkinson 18 ) ' For sit smell foe > o : ISSG ) IT4 6II exists classical solution to there unique a on Notes Good notes written on