Mausam, (1989). 131 ·136 551.509 .313 : 551.513 Topogr aphic waves in baro trop ic flow A IL KUMAR JAI 1 Meteorological Office, Agar/ala Airport, Tripura ( Receil'cd 3 M orell 1988) ••T<_ ". .... ,,'" om f"," if "l'!Tff '''' m ii 'i" '1M",!' ".ro ott "fi>f,'fl Of': t fu- ", om: If'f1:n; wtWi i ;; *R ": 'l rit 'it "fi":;fi ii 'f:T Sl'lirrr fro'lT llllrI Iff.: ff.q1' fi:' "tit l:!'f." 3f "lJ:A lNq 'If.:" t JfW II tn' ... i llq'A' :i= "r.I' 3i..,.fuf if llT ai "q llT f<rqll 1 vff'lo..rf'=f q 'Ti!:9" 1111l9- i if fr.Q1 lTlfr I . -. technique .of, Fourier series is used to study linear and non-linear effects on the In... lablilty of a baSIC state of a. topographically ro n.."t.; t wave in an inviscid baro tropic beta plane model. II, IS .. hown that analytical study on IS po-tslbl.c If amplitude of wave like perturbat io n is either an C\CIl or odd function In space about ongm. 1he study is carried out in the present paperfor former case. 1. Introduction In a series of recent pap ers (C harney and Devore 1979, Ch arne y and Strauss 19HO, lI art 1979, Deinin ger 19HI, Pedlosky 198 1), co nce pt of to pog raphic ins tab ility and theory on reso nan tt op og r ap hic waves in baroclinic and ba rotrop ic flows arc dev eloped, Holopa incn (I97H) has sho wn impo rtance and sign ificant relative co ntributio n of transient eddies in maintenance of horizontal flux of relative vorticity. Also pointed ou t by Pedlosky (19HIl, the models in the papers ci ted above suffer from either severe truncations or assumptions sometimes unrealistic. It can be argued that truncations or assumptions are no t ado pted to simplify analysis of basic vortici ty equa- tio n by all the investigators. Imposition of a constraint is fo und unav oidable for want of an additional equation or co nditio n to conclude results from the analvsis. T he governing equation cannot impose restriction on the field of pert urb ations that may' exist in the a tmosphere . used for lin ear and non-linear an alyses. H owever th e analysis. presented here, is more rigo rous. It is believed in pre sent work that interact i on between stand- ing and tr an sient eddies is functio n of t opo graphy and perturbat ion , For all type of perturbati ons that may exist in the atmos phe re, top ography need not to result instab ility. However, there may exist some per turb a- lion s th at exhibit instability due to interaction with topog ra phy. Hence, a classificati on of pert urbations is likely to be possible such that perturbati on s fro m a classifie d gro up may result in an instability. Classifying pe rtur bat ions in three groups. i.c.. wave like per turba- lions pn:,pagating in (k", I .) d irect ion with fr equ ency ;\ and eit her an even or odd or m ixed amp litude in space abo ut orig in, a linear and non-linear analysis is carried ou t for first classification in the present work . 2. TIl< model where 'I' is th e gcos tro phic stream function whose x and )' derivatives give " and - /I respectively. Th e plan etary vorticit y gradient is fi. If hn is height of the topography then The quasi-gcos t rop hic vorticity e quation for a homo- ge neous , barot ropic fluid on the /l-plane can be written in no n-di me nsiona l for m as (Ped los ky 1979) : ( ,N I a a'll a) - +- -- ----- (V'2'1' +/ly+ h) =O Ct OX ay ay OX (2, I) The atmosphere is baroclinic. Ho we ve r. the beha- viour of a barot ropic atmosphere. surely has a mapping in the baroclinic atmosphere . Hence. a result that is ob tained for ba rotropic model, sho uld be trea ted as the result that provides basic unde rs tand ing of the physics invo lved. Deininger (198 i) used the or y of pert ur bat ion with infinite series so lution of differential equation to study interaction between standing and transient eddies in the bar otropic flow in the atm osphere. He p rop osed trun - cation to make ana lysis possible. Alth ough it is pos- sible to carry out analysis for less re str ict ive truncati o n yet tr unca tion is a must for an ana lysis. The an aly sis would be s ubjected to cr iticism for any choice of finite t runc at ion. In the pr es ent paper similar theor y is (13t ) h = lIn/<n (2 .2)