Core of the magnetic obstacle

Abstract

Rich recirculation patterns have been recently discovered in the electrically conducting flow subject to a local external magnetic termed “the magnetic obstacle” (E.V. Votyakov, Y. Kolesnikov, O. Andreev, E. Zienicke, and A. Thess, Phys. Rev. Lett., vol. 98 (2007), p. 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 by both the upstream flow and the induced cross-stream electric currents, such as 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 the center of the magnetic gap, confirming the general conclusion on 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.

Keywords:

• magnetohydrodynamics
• low magnetic Reynolds number
• magnetic obstacle
• creeping flow
• recirculation patterns

Acknowledgments

This work has been performed under the UCY-CompSci project, a Marie Curie Transfer of Knowledge (TOK-DEV) grant (Contract MTKD-CT-2004-014199) and the contract of association ERB 5005 CT 99 0100 between the European Atomic Energy Community and the Hellenic Republic. This work was also partially funded under a Center of Excellence grant from the Norwegian Research Council to the Center of Biomedical Computing.

Notes

¹In the 2D simulations, the numerical mesh varied from 64² to 256². The quality of the mesh was checked by repeating the runs with doubled resolution.

²A moderate Ha range was also used in this paper in order to avoid numerical difficulties related to the resolution of Hartmann layers.