On linear and non-linear hydromagnetic fluid motion generated by oscillating solid boundaries. Part I

Abstract

In the present paper we start an investigation of the generation of second order vorticity (streaming) in an electric conducting, viscous and compressible fluid embedded in an external magnetic field. The equations used are those pertaining to the one-fluid model.

First, fairly general equations for the generation of fluid vorticity as well as magnetic vorticity are derived. By using the method of successive approximations, the systems of equations of first and second order are developed. By the use of dimensional analysis the importance in the vorticity generation of the different generating terms is briefly investigated.

Next the linear equations for two-dimensional problems are solved in the case of fluid motion above a flexible plate, vibrating in an external magnetic field.