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
theory is presented and compared to numerical experiments. To predict the
trajectories, we consider initially monopolar vortices, with a core of
potential vorticity, and calculate the evolution of the dipolar circulation
the vortex core. This multi-layer model yields analytical solutions for
period while the Rossby wave radiation is small.
The development of the dipolar circulation and corresponding vortex
are described as the results of three effects. The first and second are
what was found in earlier studies with a one-layer model: advection of
vorticity by the symmetric vortex circulation, and horizonal deformations
vortex core. In addition, when stratification is taken into account, the
of the vortex core also plays a role. This third effect is here represented
displacement of potential vorticity contours in different layers.
Examples are given for one-, two- and three-layer models and compared
numerical simulations. It is found that the analytical predictions are
for several Rossby wave periods.