Asymptotic analysis of transition to turbulence and chaotic advection in shear zonal flows on a beta-plane

The generation of narrow-band Rossby wave packets and the modulated vortex chains induced by them in a weakly-dissipative zonal flow on the beta-plane with a velocity profile in the form of a shear layer is studied. The analysis is performed within the framework of the asymptotic approach based on the distinguishing a thin critical layer inside of which the vortex chains are formed. The evolution equations, describing the simultaneous development of a wave packet envelope and vorticity perturbations in a nonlinear critical layer, are derived for a weakly supercritical flow. A transition to the complex dynamics of a wave packet (low-mode turbulence) is studied within the framework of a numerical solution of the derived equations and its mechanism is revealed. The onset of chaotic advection and anomalous diffusion of passive scalar in the critical layer is considered, and the exponent of the diffusion law is calculated.