Slow flow of a conductive liquid about a sphere containing a rotating magnetic dipole

Abstract

A number of studies (cf. [i, 2]) have examined the flow of an incompressible viscous liquid around a rotating sphere, together with magnetohydrodynamic flow around a slowly rotating sphere [3, 4]. In [5, 6] turbulent flows were considered, arising in a conductive incompressible liquid under the influence of the electromagnetic field created by a variable dipole located within a nonconducting sphere. In [5] the dipole was located in the center of the sphere, while in [6] it was shifted away from the center, leading to motion of the sphere relative to the liquid at rest at infinity. The present study will consider the problem of slow flow of a conductive incompressible viscous liquid around a sphere containing a rotating magnetic dipole. The liquid occupies all of an infinite space outside the sphere of radius a, as in [5, 6]. The problem will be solved for the case of small hydrodynamic and magnetic Reynolds numbers. The solution contains two terms of the Stokes expans ion.