Magneto-fluid dynamics of bodies in alined fields

Abstract

The motion of a perfectly conducting fluid past a fixed body in the presence of an alined magnetic field can be regarded as the limit of a number of problems, namely (i) when the fluid is a finite conductor, (ii) an unsteady problem, (iii) when themagnetic and velocity fields are not parallel at infinity. The limits of these m ore general problems agree in predicting a force on the body and on the existence of upstream and downstream wakes. However, if the magnetic field is fairly strong (i) does not predict a downstream wake while (ii) and (iii) do. An attempt to reconcile these limit results is made here. In the first part we show that the unsteady problem associated with a finitely conducting fluid and an alined field is nonunique but that by making an appeal to the theory of real fluids the conclusion of (i) and (ii) can be obtained as special cases of the general solution. In the second part the steady problem, assuming that the conductivity is finite and the magnetic field is nearly alined, is considered and it is shown that the flow fields predicted in (i) and (ii) are limiting cases of this more general problem. The manner of the changeover from the solution for (i) to that for (iii) is elucidated.