The Role of the Kelvin-Helmholtz Instability in the Evolution of Magnetized Relativistic Sheared Plasma Flows
We explore, via analytical and numerical methods, the Kelvin-Helmholtz instability in relativistic magnetized plasmas, with applications to astrophysical jets. We solve the single-fluid relativistic magnetohydrodynamic (RMHD) equations in conservative form using a scheme which is fourth-order in space and time. To invert the RMHD equations, we use a highly accurate, rapidly-convergent algorithm which improves upon such schemes as the Newton-Raphson method. Though the exact RMHD equations are marginally stable, numerical discretization renders them unstable. Artificial viscosity restores numerical stability, but also models physical processes (momentum transfer, conductivity). We use a two-dimensional slab geometry with periodic boundary conditions in both directions. The background velocity peaks along the central axis and vanishes asymptotically at the transverse boundaries. Remaining background quantities are uniform, with a flow-aligned background magnetic field. In both the linear and nonlinear analysis, we have successfully unified the HD, MHD, RHD, and RMHD regimes.
The early nonlinear regime corresponds to the formation of counter-rotating vortices, connected by filaments, which persist in the absence of a magnetic field. A magnetic field inhibits the vortices through a series of stages, namely, field amplification, vortex disruption, turbulent breakdown, and an approach to a flow-aligned equilibrium configuration. Similar stages have been discussed in MHD literature. We examine how and to what extent these stages manifest in RMHD for a set of representative field strengths. To characterize field strength, we define a relativistic extension of the Alfvenic Mach number MA. We observe close complementarity between flow and magnetic field behavior. Weaker fields exhibit more vortex rotation, magnetic reconnection, jet-broadening, and intermediate turbulence. Sufficiently strong fields (MA < 6) completely suppress vortex formation. Maximum jet deceleration, and viscous dissipation, occurs for intermediate vortex-disruptive fields, while maximum electromagnetic energy extraction occurs for the strongest fields which allow vortex formation. Our results are qualitatively similar to observations of numerous jets, including M87, whose knots may exhibit vortex-like behavior.
Highly relativistic flows destabilize the system, supporting modes with near-maximum growth at smaller wavelengths than the shear width of the velocity. This helps to explain early numerical breakdown of highly relativistic artificial viscosity simulations, a long-standing problem.