Linear and nonlinear resonant interaction of sound waves in dissipative layers

The theory of resonant nonlinear magnetohydrodynamic (MHD) waves in dissipa tive steady plasmas developed by Ballai and Erdelyi is used to study the ef fect of steady flows on nonlinear resonant heating of MHD waves in (a) line ar, (b) weakly and (c) strongly nonlinear approximations. Nonlinear connect ion formulae for slow MHD waves are derived. This nonlinear theory of drive n MHD waves is then used to study the interaction of sound waves with one-d imensional isotropic steady plasmas. We find that a steady equilibrium flow can significant influence the efficiency of resonant absorption in the con sidered limits. In the case of strong nonlinearity, the efficiency of the r esonant coupling is found to be proportional to the counterpart obtained in linear theory. The factor of proportion is approximately of the order of u nity, justifying the commonly applied linear approximations.