A NEW TECHNIQUE BASED ON THE TRANSFORMATION OF VARIABLES FOR NONLINEAR DRIFT AND ROSSBY VORTICES

The quasi-two-dimensional nonlinear equations for drift and Rossby vor tices have some stationary multipole solutions, and especially the dip ole vortex solution is railed modon. These solutions are valid only in the lowest order where the fluid velocity has a stream function. In o rder to investigate features of the multipole solutions more accuratel y, the effect of the higher order terms, for example the polarization drift in a plasma or the Coriolis force in a rotating planet, needs to be considered. It is shown that the higher order analysis through a n ew technique based on a transformation of variables is much easier tha n a straightforward iteration. The solutions in this analysis are obta ined by inverse transformation to the original coordinates, where the profiles of potentials are distorted by the effects of higher order te rms.