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

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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.