Supercritical regimes in Rossby wave propagation

The barotropic instability of Rossby wave motion is examined. The results of investigations of instability in Rossby wave motion are applicable to a description of zonal jet flows in the atmosphere and ocean. On the basis of the qualitative similarity of the physical patterns of secondary motion accompanying Rossby wave instability and jet like motions in the atmosphere and in the open ocean it is possible to relate the generation and intensification of jets to the effect of instability of a planetary wave. Using a three mode approximation, the nonlinear stability of a barotropic Rossby wave propagating amidst a constant current is analyzed. A nonlinear dynamic system in amplitude phase variables which allows a closed solution in the form of elliptical functions is formulated. An unstable case is analyzed which corresponds to a predominance of nonlinearity over dispersion and approximation formulas for the solution are obtained for this case. A qualitative analysis of stationary states of the system is performed.