Propagation of electrohydrodynamic surface waves in a conducting fluid

Abstract

A comprehensive study is made of the electrohydrodynamic surface wave phenomena in an inviscid, incompressible conducting fluid in the presence of an external steady electric field due to an arbitrary periodic surface pressure distribution. The initial value wave problem has been solved by the Laplace and the generalized Fourier transforms in conjunction with asymptotic techniques — as advanced in a previous work ofDebnath andRosenblat [12]. An explicit steady state solution related to short and long wave approximations is found. The asymptotic behaviour of the transient solution for large time is demonstrated. It is shown that there are two surface wave-trains propagating in the conducting medium, one of which corresponds to the classical surface wave train and the other is originated entirely due to the interactions of the electric field with gravity. The simultaneous effects of the electric field and surface tension on the propagation of small amplitude surface waves are analyzed. The implications of the wave solutions related to very deep and shallow fluids are explored. A discussion of the electrohydrodynamic wave motions with their characteristic features is presented.