Laminar MHD Ekman layer in differentially rotating fluid: linear teory

V. I. Pariev^1,2

¹ Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
² Lebedev Physical Institute, Moscow 117924, Russia

Abstract
An Ekman boundary layer is formed in a differentially rotating fluid near the solid end plate limiting the axial extend of the flow. The structure of such steady magnetohydrodynamic Ekman layer in a conducting incompressible liquid is considered in the presence of an axisymmetric magnetic field. The axial extend of the flow in another direction is infinite and the rotational profile far from the end plate is assumed to be Couette. The equations become linear, when the angular rotational velocity of the fluid in Couette profile differs small from the angular rotational velocity of the end plate. However, the shear of angular velocity cannot be neglected and leads to the modification of the structure of the linear Ekman layer. The width of the Ekman layer and the Ekman current decreases with increasing the strength of the component of the magnetic field normal to the surface of the end plate and increases with increasing the shear in the differential flow. When the shear exceeds a certain threshold and the magnetic field is weak enough, no steady solutions of the boundary layer type exist. Figs 9, Refs 19.