Abstract
Stationary vortex solutions of the Charney-Hasegawa-Mima equation describing planetary Rossby waves and plasma drift waves are analyzed for background flow with velocity shear. The solutions are obtained by Larichev-Reznik's method that divides the entire plane into two regions by a circle on which the internal and external solutions of linear equations are connected. The boundary conditions on the circle are satisfied correctly by adding a vorticity-free flow to the external background shear flow. Explicit flow patterns, dipolar, tripolar and quadrupolar, are given for several kinds of the background shear flows; the monopolar vortex like the Jovian Red Spot could not be obtained by this method. Another method is given, to derive a nonlinear equation for the stream function when the equilibrium density profile and shear flow in a plasma are prescribed.
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