On the analogy between streamlined magnetic and solid obstacles

TL;DR

This paper explores the analogy between magnetohydrodynamic flows with magnetic obstacles and ordinary hydrodynamic flows around solid obstacles, highlighting similarities in flow patterns and vortex behavior.

Contribution

It introduces a qualitative analogy between magnetic and solid obstacles, detailing the formation of an impenetrable core and vortex shedding in MHD flows.

Findings

Formation of an impenetrable core in MHD flow at high magnetic interaction parameter

Vortex shedding occurs when Reynolds number exceeds a critical value, similar to solid obstacles

Flow patterns exhibit similarities in electric potential and pressure contours

Abstract

Analogies are elaborated in the qualitative description of two systems: the magnetohydrodynamic (MHD) flow moving through a region where an external local magnetic field (magnetic obstacle) is applied, and the ordinary hydrodynamic flow around a solid obstacle. The former problem is of interest both practically and theoretically, and the latter one is a classical problem being well understood in ordinary hydrodynamics. The first analogy is the formation in the MHD flow of an impenetrable region -- core of the magnetic obstacle -- as the interaction parameter $N$, i.e. strength of the applied magnetic field, increases significantly. 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. In the core, closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. The second analogy is the breaking away of attached vortices from the recirculation pattern produced by the magnetic obstacle when the Reynolds number $Re$, i.e. velocity of the upstream flow, is larger than a critical value. This breaking away of vortices from the magnetic obstacle is similar to that occurring past a real solid obstacle. Depending on the inlet and/or initial conditions, the observed vortex shedding can be either symmetric or asymmetric.