| Abstract: | Approximately stationary anticyclones in shallow water on a rotating planet are studied both analytically and numerically. They consist of a monopolar part with large amplitude and a dipolar part with small amplitude, proportional to the beta parameter. An explicit solution for the dipolar part is o obtained with an arbitrary radial profile of the monopolar part. Numerical experiments show that this dipolar part accelerates or decelerates an initially circular vortex depending on the vortex size. The propagation speed is determined by a general integral relation. It is found that for the vortices to be stationary, this speed should not be close to the phase velocity of linear Rossby waves. This requires a strongly elevated surface (large amplitude). The vortices contain a core region with trapped fluid, unlike one-dimensional KdV solitons. Applications of the solution to long-lived geophysical eddies are discussed. |
