Nonlinear interaction of small-scale Rossby waves with an intense large-scale zonal flow

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