Numerical simulations of Kelvin-Helmholtz instability: a two-dimensional parametric study

TL;DR

This study uses two-dimensional numerical simulations to analyze how various physical parameters influence the Kelvin-Helmholtz instability, revealing sensitivities, phase behaviors, and implications for solar corona phenomena.

Contribution

It provides a detailed parametric analysis of Kelvin-Helmholtz instability, including effects of viscosity, flow speed, magnetic field, and phase dynamics, with implications for solar observations.

Findings

Multi-vortex phase exists between initial and final vortex states.

Phase durations approach constants at high Mach numbers in supersonic flows.

Weak magnetic fields have negligible linear coupling with KH modes.

Abstract

Using two-dimensional simulations, we numerically explore the dependences of Kelvin-Helmholtz instability upon various physical parameters, including viscosity, width of sheared layer, flow speed, and magnetic field strength. In most cases, a multi-vortex phase exists between the initial growth phase and final single-vortex phase. The parametric study shows that the evolutionary properties, such as phase duration and vortex dynamics, are generally sensitive to these parameters except in certain regimes. An interesting result is that for supersonic flows, the phase durations and saturation of velocity growth approach constant values asymptotically as the sonic Mach number increases. We confirm that the linear coupling between magnetic field and Kelvin-Helmholtz modes is negligible if the magnetic field is weak enough. The morphological behaviour suggests that the multi-vortex coalescence might be driven by the underlying wave-wave interaction. Based on these results, we make a preliminary discussion about several events observed in the solar corona. The numerical models need to be further improved to make a practical diagnostic of the coronal plasma properties.