MHD with inertia - Flow over blunt obstacles in channels

This paper treats 2-dimensional MHD flow past bluff bodies in channels for interaction numbers which are much larger than one and much smaller than the Reynolds number, when the flow is not everywhere inertialess. The analysis of Hunt and Leibovich (1967) is extended to study the inertial layer that develops at the nose of a bluff body placed in a channel. Two-term asymptotic expressions are constructed for the lift and drag forces exerted on the body. It is shown that, in general, the inertial layer induces a secondary circulatory flow around the body, the contribution of which toward the forces on the body increases with the degree of bluffness of the body but is never as large as the overall forces due to the pressure required to drive the fluid across the magnetic field. The latter forces are approached as the body becomes flatter; the analysis breaks down in the limit. This circulation is absent when there is complete symmetry about the midplane of the channel, as well as in flow past a sudden bump in one of the channel walls.