Finite amplitude effects in the propagation and interaction of m =0 torsional hydromagnetic waves

In this paper the nonlinear behaviour of the m = 0 torsional hydromagnetic wave is analyzed. Two cases have been considered: the nonlinear self-interaction of a single torsional wave and the nonlinear interaction of two identical, oppositely propagating torsional waves. In the first case the nonlinear terms in Ohm's law and the equation of motion generate a second order perturbation which accompanies the primary wave and has two components: a steady component and an oscillatory component having twice the frequency of the primary torsional wave. In the second case studied the self and cross-interactions of the two waves again generate a second order perturbation field. The existence of certain critical wavelengths, at which geometric resonances of the perturbation occur, is established.