Viscous Kelvin-Helmholtz instabilities in highly ionised plasmas

TL;DR

This study systematically investigates how viscosity affects the Kelvin-Helmholtz instability in highly ionised plasmas, revealing critical viscosity thresholds and their implications for astrophysical phenomena.

Contribution

It provides the first comprehensive numerical analysis of viscous effects on KHI across all viscosity regimes, including derivation of critical Reynolds numbers and growth time relations.

Findings

Moderate viscosities slow KHI growth and reduce roll height.

Viscosities above a critical value suppress KHI.

Derived critical Reynolds number for viscous suppression of KHI.

Abstract

Transport coefficients in highly ionised plasmas like the intra-cluster medium (ICM) are still ill-constrained. They influence various processes, among them the mixing at shear flow interfaces due to the Kelvin-Helmholtz instability (KHI). The observed structure of potential mixing layers can be used to infer the transport coefficients, but the data interpretation requires a detailed knowledge of the long-term evolution of the KHI under different conditions. Here we present the first systematic numerical study of the effect of constant and temperature-dependent isotropic viscosity over the full range of possible values. We show that moderate viscosities slow down the growth of the KHI and reduce the height of the KHI rolls and their rolling-up. Viscosities above a critical value suppress the KHI. The effect can be quantified in terms of the Reynolds number Re = U{\lambda}/{\nu}, where U is the shear velocity, {\lambda} the perturbation length, and {\nu} the kinematic viscosity. We derive the critical Re for constant and temperature dependent, Spitzer-like viscosities, an empirical relation for the viscous KHI growth time as a function of Re and density contrast, and describe special behaviours for Spitzer-like viscosities and high density contrasts. Finally, we briefly discuss several astrophysical situations where the viscous KHI could play a role, i.e., sloshing cold fronts, gas stripping from galaxies, buoyant cavities, ICM turbulence, and high velocity clouds.