The Construction of Barotropic Modons on a Sphere

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Abstract
It is shown that exact modon solutions of the barotropic vorticity equation on a sphere can be constructed. By using Legendre functions of real and complex degree and superimposing dipole and monopole streamfunctions, the zeroth, first and second derivatives of the total streamfunction can be made continuous on the boundary circle. As a necessary condition, a nonlinear constraint similar to that in the beta plane case must be satisfied. This constraint is analyzed by graphical methods, concentrating on the smallest and simplest modons it allows. A few examples of these modons are discussed in more detail. It is shown that the beta plane modons are recovered by taking the small-modon limit. Abstract It is shown that exact modon solutions of the barotropic vorticity equation on a sphere can be constructed. By using Legendre functions of real and complex degree and superimposing dipole and monopole streamfunctions, the zeroth, first and second derivatives of the total streamfunction can be made continuous on the boundary circle. As a necessary condition, a nonlinear constraint similar to that in the beta plane case must be satisfied. This constraint is analyzed by graphical methods, concentrating on the smallest and simplest modons it allows. A few examples of these modons are discussed in more detail. It is shown that the beta plane modons are recovered by taking the small-modon limit.

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