A POINT VORTEX DIPOLE MODEL OF AN ISOLATED MODON

A point vortex dipole model for an isolated modon governed by the Charney-Hasegawa-Mima (CHM) equation is developed, building on the point vortex formulation of Zabusky and McWilliams [Phys. Fluids 25, 2175 (1982)]. The model dipole is compared to the exact modon solution in order to determine parameter values for which the model dipole matches the modon's speed and far-field behavior. The model allows one to study nonuniform motions analytically. It predicts that right-moving modons in uniform motion should be stable in the sense that their paths exhibit small-amplitude oscillations in response to small perturbations of their initial orientation. It also predicts that left-moving modons in uniform motion should be unstable, being pushed into finite-amplitude motions by arbitrarily small perturbations. These predictions are confirmed by direct numerical simulation of modons evolving under the CHM equation. It is noted that although the distribution of vorticity within modons may be Lyapunov stable in nearly uniform motions, the paths of modons may be unstable to asymmetric perturbations.