Rotating hydromagnetic flow in the presence of a horizontal magnetic field

Following Hollerbach’s work (Geophys. Astrophys.Fluid Dynam., 1996) we investigate the hydromagnetic flow in a region x ≥ 0, −∞ < y < ∞ , 0 < z < 1 bounded by three electrically insulating rigid walls. The rotation vector is in the z-direction while the applied uniform magnetic field B0 is in the x-direction. Antisymmetric and symmetric cases are considered and analytical solutions are obtained for all the field variables for both the transition field regime (E1/2 ≪ Λ ≪ E1/3) and strong magnetic field regime (Λ ≫ E1/3) where Λ (=σ B2/ρΩ) is Elsasser number. Emphasis is put on the physical aspects of the problem and the meridional cir-culation pattern of electric currents. Unlike the case where a separate magnetic boundary layer exists to close the meridional electric current flux when the rotation vector and applied magnetic field are aligned, it is found that no such layer exists in the present problem; the electric currents generated in the interior and in the boundary layer regions have to be closed through interior region only. The transition field regime is characterized by the Stewartson’s double layer structure with the noted exception that the outer Stewartson layer O(E/Λ)1/2 is weak. In addition, sub-boundary layers with an axial scale equal to the corresponding boundary layer scale develop at z=0,1 for each layer. In the large magnetic field regime, while the Λ layer which replaces the inner Stewartson layer O(E1/3) satisfies the boundary condition on u-field, the thin (E/Λ)1/2 layer is necessary to satisfy the boundary condition on v and w fields.