Nonlinear coupling of MHD waves in inhomogeneous steady flows

The nonlinear coupling of MHD waves in a cold (β = 0) compressible plasma with a smoothly inhomogeneous low-speed steady flow directed along the magnetic field is considered. The effect is similar to Alfvèn 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 thewavenumber of the source Alfvén waves. The efficiency of the generation is defined by theAlfvénwave amplitude and the transversal spatial scale of the flow inhomogeneity. The secular growth of density perturbations, connectedwith 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.