Dispersive stabilization of the inverse cascade for the kolmogorov flow

It is shown by perturbation techniques and numerical simulations that the inverse cascade of kink-antikink annihilations, characteristic of the Kolmogorov flow in the slightly supercritical Reynolds number regime, is halted by the dispersive action of Rossby waves in the β-plane approximation. For β → 0, the largest excited scale is ∝ ln 1/β and differs strongly from what is predicted by standard dimensional phenomenology which ignores the depletion of nonlinearity.