Instability in electromagnetically driven flows Part I

TL;DR

This paper investigates the instability phenomena in magnetohydrodynamic flows driven by traveling magnetic fields, revealing a saddle-node bifurcation and bistability between different flow regimes, with implications for flow control.

Contribution

It characterizes the bifurcation and stability of MHD flows driven by TMF, highlighting the role of magnetic flux expulsion and bistability in flow transitions.

Findings

Flow undergoes saddle-node bifurcation at high Rm or pressure gradient.

Bistability exists between Poiseuille-like and Hartman-like regimes.

Magnetic flux expulsion influences flow stability and transition.

Abstract

The MHD flow driven by a travelling magnetic field (TMF) in an annular channel is investigated numerically. For sufficiently large magnetic Reynolds number Rm, or if a large enough pressure gradient is externally applied, the system undergoes an instability in which the flow rate in the channel dramatically drops from synchronism with the wave to much smaller velocities. This transition takes the form of a saddle-node bifurcation for the time-averaged quantities. In this first paper, we characterize the bifurcation, and study the stability of the flow as a function of several parameters. We show that the bifurcation of the flow involves a bistability between Poiseuille-like and Hartman-like regimes, and relies on magnetic flux expulsion. Based on this observation, new predictions are made for the occurrence of this stalling instability.