Magnetohydrodynamic shear layers in a rapidly rotating plane layer

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Abstract
We consider free shear layers in a rapidly rotating fluid layer defined by |z| < 1. At z = ± 1 we impose the velocity v = Fs(x) ± Fa(x). Discontinuities in Fs and Fa then turn out to induce vertical shear layers throughout the fluid. A discontinuity in Fs induces two layers of thicknesses E ¼ and E ⅓; a discontinuity in Fa induces one layer of thickness E ⅓. The Ekman number E is an inverse measure of the rotation rate. We demonstrate that these shear layers are in fact the same as the classical Stewartson layers in cylindrical geometry. We next consider the effect of imposing a magnetic field across these shear layers. In the limit of small magnetic Reynolds number Rm , we demonstrate that for Λ≥E ⅓ all of the previous shear layer structure is ultimately suppressed, where the modified Elsasser number Λ(≡Rm ) is a measure of the strength of the imposed field. The various transitions between the non-magnetic and the fully magnetic regimes are discussed in some detail.

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