Stability of Hartmann flow with the convective approximation

TL;DR

This paper analyzes the linear stability of Hartmann flow under a transverse magnetic field using a convective approximation, deriving equations for perturbations and confirming instability conditions that align with experimental observations.

Contribution

It introduces a new linear stability analysis of Hartmann flow in a convective approximation, deriving an instability equation and identifying conditions for flow instability.

Findings

Derived an equation for the instability increment.

Identified nonexcitation conditions for perturbation modes.

Confirmed that instabilities agree qualitatively with experimental data.

Abstract

This research is focused on linear analysis of a plane-parallel flow stability in a transverse magnetic field (Hartmann flow) within a convective approximation. We derive and solve equations describing the perturbation growth. Perturbation modes and their nonexcitation conditions have been determined. An equation for the instability increment has been derived and it is shown that the equation has an unstable root. Additionally, we show that the resulting instabilities qualitatively agree with the experimental data.