Intense vortex motion in a stratified fluid on the beta-plane: an analytical theory and its validation

Abstract

This paper deals with the self-induced translation of intense vortices on the β-plane in the framework of the multi-layer quasi-geostrophic approximation. An analytical theory is presented and compared to numerical experiments. To predict the vortex trajectories, we consider initially monopolar vortices, with a core of piecewise-constant potential vorticity, and calculate the evolution of the dipolar circulation which advects the vortex core. This multi-layer model yields analytical solutions for a period while the Rossby wave radiation is small.

The development of the dipolar circulation and corresponding vortex translation are described as the results of three effects. The first and second are similar to what was found in earlier studies with a one-layer model: advection of the planetary vorticity by the symmetric vortex circulation, and horizonal deformations of the vortex core. In addition, when stratification is taken into account, the vertical tilting of the vortex core also plays a role. This third effect is here represented by the relative displacement of potential vorticity contours in different layers.

Examples are given for one-, two- and three-layer models and compared with numerical simulations. It is found that the analytical predictions are good for several Rossby wave periods.