NONLINEAR-INTERACTION OF SMALL-SCALE ROSSBY WAVES WITH AN INTENSE LARGE-SCALE ZONAL FLOW

The system of Rossby waves is unstable with respect to modulations. Th is instability results in the generation of a large-scale zonal flow w ith zero mean vorticity. It is shown that in both stable and unstable situations, a finite-time singularity formation takes place in the sys tem. Such a singularity has the form of peaks on the vorticity profile of the zonal flow. The situation is also considered when some zonal f low with nonzero mean vorticity is initially present. Solitary-wave so lutions appropriate for the description of nonlinear behavior of such systems are found. In the case of weak mean vorticity of the zonal flo w, the solitons break and the singularities develop. If the mean vorti city is strong, then the evolution of the system can be considered as the dynamics of a soliton gas. Soliton dynamics possesses some interes ting properties, such as formation of soliton pairs and annihilation o f solitons during collision.