Anisotropic transient wave motions in a conducting fluid under uniform magnetic and current fields

An initial value investigation into the development of two-dimensional anisotropic surface waves generated by a harmonically oscillating pressure distribution acting on the undisturbed free surface of an inviscid, incompressible homogeneous and electrically conducting fluid is made in this paper in considerable detail. The problem is solved by the use of generalized function treatment in conjunction with asymptotic methods. An asymptotic solution of the problem related to some physically realistic pressure distributions is presented. It is shown that an ultimate steady state is set up in the limit. Two limiting cases such as (1) very deep fluid and (2) very shallow fluid, which are of particular interest have been examined with some emphasis. Finally, the effects of the imposed magnetic and current fields as well as the surface tension on the wave motions has been examined in some detail. Additionally, it is shown that the present method of solution provides an interesting example of the applicability of the generalized function method in problems of magnetohydrodynamics.