Generation of Zonal Flows in a Rotating Self-Gravitating Fluid

We demonstrate the possibility of generation of zonal (shear) flows in a rotating self-gravitating fluid. A set of equations describing the nonlinear interaction between a large-scale zonal flow (ZF) and a small-scale drift-gravity wave is derived. A nonlinear dispersion relation is obtained, from which the possible instability of the ZF follows. The necessary condition for instability in the space of wave numbers of the drift-gravity wave, as well as the instability threshold for the wave amplitude, are obtained. The growth rate of the modulation instability of ZF is found. The generation of ZFs is due to the Reynolds stresses produced by finite amplitude drift-gravity waves.