Strong Potential Magnetic Field Influence on Slightly Differentially Rotating Spherical Shell

An electrically conducting viscous fluid-filled spherical shell is permeated by an axisymmetric strong potential magnetic field with large Elssaser number λ2 ≫ 1. We describe analytically the steady flow driven by a slightly faster rotation of the conducting inner boundary of the shell. The main flow is controlled by Ekman-Hartmann boundary layers with a small thickness δ/λ, where δ2is the Ekman number. Asymptotics based on small λ−1 ≪ 1 reveal the nature of a free shear layer O((δ/λ)1/2) and a super-rotation that allows a part of the fluid to rotate faster than the inner sphere. The free shear is following an imposed field line that is tangent to the inner or outer sphere. Meridional flux is concentrated in the shear and boundary layers. Fluid tends to rotate with the inner sphere and to expel azimuthal magnetic field from an\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$ \ell $$ \end{document}-region restricted by the free shear in the spherical shell.