Magnetohydrodynamic flows of a perfectly conducting, viscous fluid

Abstract

The paper considers the flow of an incompressible, viscous, perfectly conducting fluid past a fixed obstacle in the presence of an applied magnetic field which is parallel to the stream at large distances from the obstacle. A simple transformation of the fluid velocity and the total head enables the magnetohydrodynamic flow past the obstacle to be determined from the corresponding flow of a nonconducting fluid past the same obstacle but with a reduced main-stream velocity. The method is illustrated by considering the flows past a sphere, a circular cylinder and a semi-infinite flat plate for different field strengths. The drag on the sphere is plotted as a function of the field strength for a fixed Reynolds number. The patterns of the flow past a circular cylinder are sketched and an inference is made to the way in which disturbances can propagate upstream for the case when the main-stream velocity is less than the Alfvén speed. These give rise in the first instance to a separation bubble upstream of the cylinder. Finally the range of applicability of familiar high Reynolds number approximations to magnetohydrodynamic flows is discussed. In particular, if the main-stream velocity is equal to the Alfvén speed, the boundary-layer approximation is shown to be no longer valid.