Inflection point instability in Hartmann channel flow with variable electric conductivity

Abstract

The stability of a flow of an electrically conducting, incompressible fluid in a channel with an imposed uniform wall-normal magnetic field and electrically insulating walls is studied using linear stability analysis and direct numerical simulations. The novelty of the system, which differentiates it from the classical Hartmann channel flow, is that, as in some technological applications of liquid metals, the electric conductivity and viscosity of the fluid vary across the channel. This variation is found to have a strong influence on the stability characteristics of the flow. Specifically, a linear variation in electric conductivity significantly alters the base velocity profile, leading to pronounced asymmetry and the development of inflection points. When this transformation is sufficiently strong, the flow becomes linearly unstable at Reynolds numbers much lower than the threshold for the linear instability of the Hartmann channel flow. The instability exhibits distinct features: a large typical axial wavelength and the localization of perturbation growth in the channel core. The characteristics of this instability suggest a mechanism similar to the classical inviscid inflection-point instability of one-dimensional velocity profiles. The resulting transition to turbulence is demonstrated in direct numerical simulations.