Inverse cascade and wave condensate in mesoscale atmospheric turbulence

It is shown that an inverse cascade of the turbulence of inertio-gravity waves produces a long-scale wave condensate. A new nonlinear equation is derived for long waves on rotating shallow water. It is proven that steady localized solutions are absent and that the condensate (a uniform inertial oscillation) is stable with respect to small perturbations. Wave self-interaction could not thus stop an inverse cascade of mesoscale geophysical turbulence. The implication of the existence of a condensate for the problem of tidal dissipation and retardation of the Earth's rotation is discussed.