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<br />. <br /> <br />.i <br />- <br /> <br />- 49 - <br /> <br /> <br />. <br />t <br />L <br /> <br />~ <br /> <br />the ridge and the z-axis vertically upwards. <br /> <br />,. <br />L <br /> <br />For two dimensional, inviscid, steady flow the vorticity equation can be <br /> <br />written in the form <br /> <br />II <br />L <br /> <br />~ <br /> <br />i_ <br /> <br />a(~ . V)~ + an{V . v) -a3Vp x Vp = 0 <br /> <br />(3.1) <br /> <br />,. <br />L <br /> <br />where, <br /> <br />p is the density of the air and a = IIp, v is the velocity of the air <br />x-z plane (= ui.+ wk), n = (~u - ~) j = n; and p is the pressure. <br />- - - aZ aX - ~ <br /> <br />in the <br /> <br />. <br />t" <br />........ <br /> <br />From the continuity equation V . (pv) = 0 we have: <br /> <br />II <br />e <br /> <br />av . Vp = -v . v <br /> <br />. (3.2) <br /> <br />i. <br />f <br />~ <br /> <br />so the first two terms in eqn. (3.l) become <br /> <br />\I <br />0:: <br />.l- <br /> <br />a[(v . V)~ + ~(V . v)] = {v . V)an <br /> <br />(3.3) <br /> <br />II <br />.... <br />i-- <br /> <br />If the pressure is p and the temperature T, <br /> <br />il <br />.( <br /> <br />ap = RT <br /> <br />(3.4) <br /> <br />il <br />I <br /> <br />where R is the gas constant for dry air, so that the baroclinic term in eqn. <br /> <br />'I <br />1! <br /> <br />(3.1) can be written as <br /> <br />II <br />i"" <br />, <br />.... <br /> <br />-a3Vp x Vp = aRVT x V(ln p) <br /> <br />(3.5) <br /> <br />II <br />r <br /> <br />The potential temperature e is defined as <br /> <br />~ <br />.\- <br /> <br />R/c <br />e = T(Pr/p) P <br /> <br />(3.6) <br /> <br />\1 <br />~ <br />