Effect of the transverse magnetic field on the Kelvin–Helmholtz instability of the supersonic mixing layer

Abstract

The Kelvin–Helmholtz instability (KHI) stems from the velocity shear in a single continuous fluid or a velocity difference across the interface between two distinct fluids. The effect of the transverse magnetic field on the KHI of the supersonic mixing layer is investigated by numerical method. An algorithm with corner-transport-upwind and constrained-transport is used to solve the equations of magnetohydrodynamic (MHD). The evolutions of vorticity, pressure, and shock-vortex structure of the supersonic mixing layer with and without the magnetic field are studied qualitatively and quantitively. The suppression mechanism of the transverse magnetic field on the KHI is analyzed from the aspects of magnetic pressure and magnetic tension, respectively. The results show that the transverse magnetic field has a significant influence on the evolution of shock-vortex structure in the supersonic mixing layer. The magnetic pressure makes the vorticity deposition at the shear layer, and the magnetic tension produces an anti-bending torque on the shear layer. Under these two kinds of effects, the instability of the shear layer is suppressed effectively, and a long-standing banded structure of the shear layer is formed and teared later, which results in a “fishhook-like” structure occurred. Moreover, the transverse magnetic field inhibits the formation of the high-convection Mach value (Mc) regions, which effectively inhibits the formation of shocklets. In addition, with the effect of the magnetic field, a premature laminar-turbulent transition is stimulated at the core region of the vortex structure.