Gradient adjustment in an axisymmetric vortex
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We consider gradient adjustment in an axisymmetric vortex. From an initially unbalanced state, the final adjusted state is obtained. Initially, the geopotential is flat and the velocity field is given by the Rankine vortex. (Note: To view the equation, open the pdf of the document.) We derive a system of equations governing the final adjusted state. This system of equations is solved numerically using the shooting method. We also present solutions for the geostrophic adjustment problem and compare these to the solutions for the gradient adjustment problem. In the gradient adjustment case, the ...