Instabilities of Shercliff and Stewartson layers in spherical Couette flow

TL;DR

This paper investigates the stability of Shercliff and Stewartson layers in spherical Couette flow under magnetic and rotational influences, revealing how their interaction affects flow stability.

Contribution

It provides a comparative analysis of magnetic and rotational effects on layer instabilities in spherical Couette flow, including mixed cases.

Findings

Same direction rotation can destabilize layers

Opposite direction rotation stabilizes layers

Magnetic and rotational effects interact complexly

Abstract

We explore numerically the flow induced in a spherical shell by differentially rotating the inner and outer spheres. The fluid is also taken to be electrically conducting (in the low magnetic Reynolds number limit), and a magnetic field is imposed parallel to the axis of rotation. If the outer sphere is stationary, the magnetic field induces a Shercliffe layer on the tangent cylinder, the cylinder just touching the inner sphere and parallel to the field. If the magnetic field is absent, but a strong overall rotation is present, Coriolis effects induce a Stewartson layer on the tangent cylinder. The non-axisymmetric instabilities of both types of layer separately have been studied before; here we consider the two cases side by side, as well as the mixed case, and investigate how magnetic and rotational effects interact. We find that if the differential rotation and the overall rotation are in the same direction, the overall rotation may have a destabilizing influence, whereas if the differential rotation and the overall rotation are in the opposite direction, the overall rotation always has a stabilizing influence.