Selection of a radial wavelength of zonal flows

The nonlinear dynamics of coherent zonal flows is studied with periodic boundary conditions. We study nonlinear differential equations of zonal flows, which were previously derived in an analytic wave-kinetic model. Competition between the short wavelength zonal flow and the long wavelength zonal flow is studied. Although many stable stationary solutions are allowed, the radial periodicity length turns out to be a value around a particular length, when random small amplitude perturbations are chosen as the initial flow state.