Generalized spectra of slightly nonlinear Rossby waves

An important feature of the evolution of systems of slightly non-linear Rossby waves is an intensive transfer of energy to the zonal component of movement, that is, to wave vectors having a predominantly meridional direction. The spectrum of a stationary zonal flow, proportional to the Dirac delta equation, is shown to be a solution of the kinetic equation for Rossby waves. An equation is derived describing the evolution of the spectrum of waves against the background of zonal flow, as well as an equation for the entropy of such a system. The intensive transfer of energy to wave vectors predominantly of a meridional direction is thought not to contradict the tendency of the system to thermodynamic equilibrium.