Vorticity generation in creeping flow past a magnetic obstacle

The generation of vorticity in the two-dimensional creeping flow of an incompressible, electrically conducting viscous fluid past a localized magnetic field distribution is analyzed under the low magnetic Reynolds number approximation. It is shown that the Lorentz force produced by the interaction of the induced electric currents with the nonuniform magnetic field acts as an obstacle for the flow, creating different steady flow patterns that are reminiscent of those observed in the flow past bluff bodies. First, analytic solutions are obtained for a creeping flow past a magnetic point dipole, modeled as a Gaussian distribution. Using a perturbation scheme, the vorticity is expressed as an expansion in the small Reynolds number, and first- and second-order approximations are calculated. The induced magnetic field, pressure, and stream function are also determined. Further, full numerical finite difference solutions are obtained for a uniform creeping flow past a finite size magnetic field distribution produced by a square magnetized plate. Hartmann numbers in the range 1< or =Ha< or =100 are explored. Depending on the strength of the magnetic force, stagnation zones or steady vortical structures are obtained. The analysis contributes to the understanding of flows in nonuniform magnetic fields and flows produced by localized forces.