  The flow transformation and the generation of vortex structures by a strong
magnetic dipole field in a liquid metal duct flow is studied by means of
three-dimensional direct numerical simulations. The dipole is considered as the
paradigm for a magnetic obstacle which will deviate the streamlines due to
Lorentz forces acting on the fluid elements. The duct is of square
cross-section. The dipole is located above the top wall and is centered in
spanwise direction. Our model uses the quasi-static approximation which is
applicable in the limit of small magnetic Reynolds numbers. The analysis covers
the stationary flow regime at small hydrodynamic Reynolds numbers Re as well as
the transitional time-dependent regime at higher values which may generate a
turbulent flow in the wake of the magnetic obstacle. We present a systematic
study of these two basic flow regimes and their dependence on Re and on the
Hartmann number Ha, a measure of the strength of the magnetic dipole field.
Furthermore, three orientations of the dipole are compared: streamwise,
spanwise and wall-normal oriented dipole axes. The most efficient generation of
turbulence at a fixed distance above the duct follows for the spanwise
orientation, which is caused by a certain configuration of Hartmann layers and
reversed flow at the top plate. The enstrophy in the turbulent wake grows
linearly with Ha which is connected with a dominance of the wall-normal
z-derivative of the streamwise velocity.
