MHD oseenlet and double wake of a rising sphere under a strong vertical magnetic field

K. Ueno¹ - H. Yasuda²

¹ Department of Aerospace Engineering, Tohoku University, 980-8579 Sendai, JAPAN
² Department of Adaptive Machine Systems, Osaka University, 565-0871 Suita, JAPAN

Abstract
A flow field of an electrically conducting fluid around a rising sphere is discussed. An asymptotic solution at a large Hartmann number is proposed. A function with a singularity called MHD oseenlet is derived. It gives a double wake unique to MHD flows. Its flow rate across the horizontal plane is a finite value in contrast to the divergent flow rate for stokeslet and zero flow rate for source doublet. We obtain the flow field around a sphere in a series of MHD oseenlet and its derivatives. Fluid in the cone-shaped near wake moves with the rising sphere. The vertical height ±0.1a\Ha of the near wake is much larger than its radius a. In far wake, the flow field is reduced to the MHD oseenlet. Tables 2, Figs 5, Refs 8.