Stability of an hypersonic magnetohydrodynamic shock wave

The shape of the shock wave formed by an hypersonic conducting flow around a plane or axisymmetric obstacle is determined by the velocity at infinity and the Lorentz force generated by a magnetic field generated within the body. This shape is described by a nonlinear differential equation. When linearized near the trivial shock wave (the boundary of the obstacle), it becomes amenable to a stability analysis. The study is conveniently separated in the regions where the slope of the body is not very small and the flatter sections. In both cases the main parameter is the sign of the Lorentz force; stability generally occurs when it presses the fluid inwards, but the precise criteria depend also on several other parameters.(c) 2023 Elsevier B.V. All rights reserved.