Experimental study of a vortex in a magnetic field

Abstract

It is well-known that magnetohydrodynamic (MHD) flows behave differently from conventional fluid flows in two ways: the magnetic field makes the flow field anisotropic in the sense that it becomes independent of the coordinate parallel to the field; and the flow of liquid across the field lines induces an electric current, leading to ohmic damping. In this paper, an experimental study is presented of the long-time decay of an initially three-dimensional flow structure subject to a steady magnetic field, when the ratio of the electromagnetic Lorentz forces to the nonlinear inertial forces, quantified by the magnetic interaction parameter, N₀, takes large as well as moderate values. This investigation is markedly different from previous studies on quasi-two-dimensional MHD flows in thin layers of conducting fluids, where only Hartmann layer friction held the key to the dissipation of the flow.

The initial ‘linear’ phase of decay of an MHD flow, characterized by dominant Lorentz forces and modelled extensively in the literature, has been observed for the first time in a laboratory experiment. Further, when N₀ is large compared to unity, a distinct regime of decay of a vortex follows this linear phase. This interesting trend can be explained in terms of the behaviour of the ratio of the actual magnitudes of the Lorentz to the nonlinear inertial forces – the true interaction parameter – which decreases to a constant of order unity towards the end of the linear phase of decay, and remains invariant during a subsequent ‘nonlinear’ phase.