Nonlinear coupling of MHD waves in inhomogeneous steady flows.

The nonlinear coupling of MHD waves in a cold (beta = 0) compressible plasma with a smoothly inhomogeneous low-speed steady flow directed along the magnetic field is considered. The effect is similar to Alfven wave phase mixing in a static, inhomogeneous medium and leads to the production of steep transversal gradients in the plasma parameters, which increases dissipation. Transversal gradients in the total pressure, produced by phase mixing, lead to the secular generation of obliquely propagating fast magnetosonic waves, at double the frequency and the wavenumber of the source Alfven waves. The efficiency of the generation is defined by the Alfven wave amplitude and the transversal spatial scale of the flow inhomogeneity. The secular growth of density perturbations, connected with fast waves, takes place for flow speeds that are considerably below the thresholds of the Kelvin-Helmholtz and negative energy wave instabilities. The initial stage of the nonlinear generation of the fast waves is considered analytically and illustrated by numerical simulations.