A Series Solution for the Barotropic Vorticity Equation and its Application in the Study of Atmospheric Vortices

Abstract

A method to obtain a series solution for the barotropic non-divergent, vorticity equation is given and is applied to the case of a vortex.A formula that gives the development of a symmetrical vortex as a function of radius, maximum velocity and latitude is obtained. A numerical example is worked out.The convergence of the series solution for the general case is discussed and shown to depend on the scale of motion to be forecast and conclusions are drawn regarding time-steps used in a forecast and the smoothing of the initial map.The possibility of improving a forecast and reducing the number of time-steps used in it by the application of this series solution, follows as a general conclusion.Finally, a theorem that gives the scaling of the variables in an experimental model of a barotropic flow is obtained. p I , = =aay/2xat, etc. 'Tellus VIII (1956), 3

A new approximation for the dynamics of topographic Rossby waves

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Angular momentum dynamics and the intrinsic drift of monopolar vortices on a rotating sphere

“…The subject of coupling of monopolar vortices to waves on a ␤-plane has been subject of an extensive branch of the geophysical fluid dynamics literature. 22,[39][40][41][42][43][44][45][46][47][48][49] It has been found that with increasing intensity of the vortex, the dispersion decay of the vortex slows down substantially 20,50-52 and perturbation analysis based solutions describing stationary, i.e., nonradiating, anticyclonic monopolar vortices on the ␤-plane have been published. 26 The dynamics of the structure of the vortices on the rotating sphere lies outside the scope of the work presented here.…”

Baroclinic vortices over a sloping bottom

“…The latter was first postulated by Rossby (1948) who noted that a vortex causes a deflection of the mean PV field and thus wil tend to migrate meridionally to reduce this deflection. Adem (1956) showed by means of a Taylor expansion in time that a cyclonic vortex drifts initially to the northwest.…”