Alfv\'en waves at low magnetic Reynolds number: Transitions between diffusion, dispersive Alfv\'en waves and nonlinear propagation

TL;DR

This study investigates the production and behavior of Alfvén waves in low magnetic Reynolds number liquid metal experiments, identifying linear diffusive and dispersive regimes and observing nonlinear wave phenomena relevant to astrophysical and geophysical processes.

Contribution

The paper introduces a wave-bearing extension of low-Rm MHD theory and demonstrates experimental production of diffusive, dispersive, and nonlinear Alfvén waves in liquid metals.

Findings

Identification of diffusive and propagative regimes of AW at low Rm

Experimental validation of the model up to Jameson number 0.85

Observation of nonlinear wave behavior near resonance J a=1

Abstract

This paper seeks whether Alfv\'en waves (AW) can be produced in laboratory-scale liquid metal experiments, \emph{i.e.} at low-magnetic Reynolds Number ($R\!m$). AW are incompressible waves propagating along magnetic fields typically found geo and astrophysical systems. Until now, only faint linear waves have been experimentally produced in liquid metals because of the large magnetic dissipation they undergo when $R\!m\ll1$. Yet, controlling laboratory AW could emulate such far remote processes as anomalous heating in the solar corona, oscillations of the Earth inner core or turbulence in the solar wind. To answer this question, we force AW with an AC electric current in a liquid metal channel in a transverse magnetic field. We derive a wave-bearing extension of the usual low$-R\!m$ MHD approximation to identify two linear regimes: The purely diffusive regime exists when $N_\omega$, the ratio of the oscillation period to the timescale of diffusive two-dimensionalisation by the Lorentz force, is small. The propagative regime is governed by the ratio of the forcing period to the AW propagation timescale which, we call the Jameson number $J\!a$ after Jameson (1964), JFM. In this regime, AW are dissipative and dispersive as they propagate more slowly where velocity gradients are higher. Both regimes are recovered in the FLOWCUBE experiment, in excellent agreement with the model up to $J\!a \lesssim 0.85$ but near the $J\!a=1$ resonance, high amplitude waves become clearly nonlinear. Hence, in electrically driving AW, we were able to produce some of the propagative, diffusive and nonlinear processes of astro and geophysical AW.