Rapid beat generation of large-scale zonal flows by drift waves: a nonlinear generic paradigm

The generalized Charney-Hasegawa-Mima equation is unstable to a four wave modulational instability whereby a coherent, monochromatic drift wave can drive a band of modes and associated zonal flows unstable. Although initially the fastest growing modes dominate, a secondary nonlinear instability later drives the longest wavelength zonal flow and its associated sidebands at twice the growth rate of the fastest growing modulationally unstable modes. This results in a direct transfer from strongly unstable short wavelength modes to the weakly unstable long wavelength modes, which drains the short wavelength pump energy. A related but less efficient direct enstrophy cascade generates very short wavelength modes lying outside the band of modulationally unstable modes.