On the stability of equivalent modons

In the framework of the equivalent barotropic dynamics, we show that the kinetic energy and enstrophy a small scale perturbation superimposed on a large scale solitary wave do not grow in time as long as the perturbation scale remains much less than that of the wave. This property is proved to hold for the equivalent modons of Flierl et al. which therefore turn out to be resistant to small scale perturbations. These conclusions appear to explain the numerical results of McWilliams et al. on non divergent modons.