Nonlinear wave interaction in a self-gravitating fluid

Summary form only given, as follows. The theory of the nonlinear resonant wave interaction is applied to the problem of a self-gravitating, rotating, astrophysical medium. Using the standard fluid equations (the continuity equation, the equation of motion, and the Poisson equation for the gravity potential), a high order nonlinear partial differential equation for the gravity potential is derived comprising nonlinearity of the vector-type (or the Poisson bracket type). The three-wave nonlinear interaction is studied for waves satisfying the resonant conditions for wave vectors and frequencies. This yields a set of three equations for the time evolution of the wave amplitudes, with the coupling coefficients that have been discussed. The intermediate mode is shown to act as a pump, resulting in the direct (towards larger values of the wave numbers) and inverse (towards smaller values of the wave numbers) cascading of the wave energy. The latter could finally lead to the formation of structures (clumps, vortices, zonal flows) in the system. The coupling coefficients are discussed for physical parameters that are valid for proto-galaxies and interstellar clouds in the pre-stellar stage of evolution.