Two-Dimensional Kelvin-Helmholtz Instability with Anisotropic Pressure

TL;DR

This work investigates Kelvin–Helmholtz instability in dilute, collisionless plasmas using Chew–Goldberger–Low (CGL) anisotropic pressure theory to quantify the role of pressure anisotropy in linear growth and nonlinear saturation. The authors solve a $9\times9$ hyperbolic CGL system with a stiff relaxation term $\tau$, comparing against standard MHD; they perform 2D simulations with smooth shear profiles and both aligned and anti-aligned magnetic fields, validated by linear theory. Key findings show the largest growth rates and magnetic activity in the MHD limit, while finite anisotropy reduces reconnection and island formation by allowing energy to reside in parallel/perpendicular pressure channels; anisotropy evolves from mirror-dominated in the linear phase to firehose-dominated in nonlinear stages. These results have implications for turbulence and reconnection in the heliosheath and similar dilute-plasma environments, and they motivate extending the analysis to fully 3D configurations and to contexts such as accretion disks and magnetic reconnection with particle energization. The study also notes limitations of the CGL model, such as inaccuracies in mirror-instability thresholds, and outlines future directions toward more realistic, three-dimensional analyses and observational connections.

Abstract

The Kelvin-Helmholtz (KH) instability occurs in multiple heliospheric (solar-wind stream interfaces, planetary magnetospheres, cometary tails, heliopause flanks) and interstellar (protoplanetary disks, relativistic jets, neutron star accretion disks) environments. While the KH instability has been well-studied in the magnetohydrodynamic (MHD) limit, only limited studies were performed in the collisionless regime, which is conducive to development of anisotropic pressures. Collisionless plasmas are often described using the Chew Goldberger and Low (CGL) equations which feature an anisotropic pressure tensor. This paper presents a comprehensive analysis of the CGL version of the KH instability using linearised and numerical techniques. We find that the largest growth rates and the greatest incidence of magnetic effects occur in the MHD limit. In the large relaxation time CGL limit, part of the energy goes into the formation of pressure anisotropies, resulting in smaller amounts of energy being available for bending the field lines. Consequently, when we cross-compare CGL and MHD simulations that are otherwise identical, the current densities are largest in the MHD limit, and the largest magnetic islands also form in that limit. Early and late time formation of pressure anisotropies have also been studied. We also find that the strongest trend for forming intermittencies in the flow also occurs in the MHD limit. The paper also discusses possible consequences of our results for turbulence and reconnection in the heliosheath (the layer between the solar wind termination shock and the heliopause).

Figures (12)

• Figure 1: Simulation setup for the 2D KH instability, showing the domain, initial velocity, density, pressure, magnetic field configuration, and flow directions. Panel (a) illustrates the aligned magnetic field configuration, with magnetic field vectors pointing to the right throughout the domain, while panel (b) shows the anti-aligned configuration, where the magnetic field vectors point to the right in the central region and to the left in the upper and lower regions.
• Figure 2: Density ($\rho$), pressure anisotropy ($A = p_\perp / p_\parallel$), current density ($J_z$), magnetic energy ($B_x^2 + B_y^2$), and total gas pressure $\bigl[(p_\parallel + 2p_\perp)/3\bigr]$ at early time ($t=7.2$, top row) and late time ($t=12.0$, bottom row) for the simulation with an anti-aligned magnetic field and CGL relaxation time $\tau = 5.0$.
• Figure 3: Same as Figure \ref{['fig_2']}, but for a CGL relaxation time $\tau = 10^{-5}$, which corresponds to the MHD limit.
• Figure 4: Same as Figure \ref{['fig_2']}, but for the aligned magnetic field simulation.
• Figure 5: Same as Figure \ref{['fig_4']}, but for a CGL relaxation time $\tau = 10^{-5}$, which corresponds to the MHD limit.