Generation of self-excited Rossby wave-modes due to their interaction with the common critical layer of a barotropically unstable stratified zonal flow is studied. The evolution equations governing the simultaneous development of the wave amplitudes and vorticity perturbations inside the nonlinear critical layer are derived for a weakly supercritical flow. The scenarios of the instability development and equilibrium states of generating the waves emerging successively as the supercriticality is increased have been studied within the frame of qualitative and numerical analysis of the derived equations.
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