Stationary Vortices of Elliptic Boundary in Drift and Geostrophic Shear Flows

Abstract

An analytic solution of the Charney-Hasegawa-Mima equaiton, a two-dimensional nonlinear equation describing geostrophic Rossby flow and plasma drift flow, is given which represents a stationary vortex of an elliptic boundary in a background flow having a linear shear. The solution is obtained through an appropriate ansatz for the arbitrary function of integration of the stationary equation. Three types of vortices emerge according to the chioce of parameters which characterize the distribution of vorticity: a generally asymmetric dipole inside the boundary ellipse E, a monopole inside E, and a larger dipole lying across E.