Rich recirculation patterns have been recently discovered in the electrically conducting flow subject to a local external magnetic termed "the magnetic obstacle" [Phys. Rev. Lett. 98 (2007), 144504]. This paper continues the study of magnetic obstacles and sheds new light on the core of the magnetic obstacle that develops between magnetic poles when the intensity of the external field is very large. A series of both 3D and 2D numerical simulations have been carried out, through which it is shown that the core of the magnetic obstacle is streamlined both by the upstream flow and by the induced cross stream electric currents, like a foreign insulated insertion placed inside the ordinary hydrodynamic flow. The closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. New recirculation patterns not reported before are found in the series of 2D simulations. These are composed of many (even number) vortices aligned along the spanwise line crossing the magnetic gap. The intensities of these vortices are shown to vanish toward to the center of the magnetic gap, confirming the general conclusion of 3D simulations that the core of the magnetic obstacle is frozen. The implications of these findings for the case of turbulent flow are discussed briefly.

14 pages, 9 figures, submitted to Journal of Turbulence