Ekman-Hartmann layer on a free surface (Q1090573)

The Ekman-Hartmann boundary layer at a free surface of rotating, electrically conducting, barotropic fluid is analyzed. The fluid motions are driven by applying stresses at the free surface. The flow is supposed to be linear, steady and axisymmetric. The applied magnetic field and the rotation vector are in the vertical direction. Contrary to the hydrodynamic case where the horizontal mass flux vector in the Ekman layer is perpendicular to the applied stress, the horizontal mass flux vector \(^{\to}_ E\) in the Ekman-Hartmann layer has components parallel and perpendicular to the stress vector. Infact, for \(\alpha\geq 1\) where \(\alpha\) is the magnetic interaction parameter, the net horizontal mass transport is mostly in a direction parallel to the stress vector. The net horizontal electric current flux in the Ekman-Hartmann layer is 90\(\circ\) to the right of net horizontal fluid flux vector. Both the Ekman suction and the Hartmann current are inhibited by the magnetic field for \(\alpha\geq 1\). The Ekman-Hartmann compatibility conditions are also presented.