Role of the Kelvin-Helmholtz instability in the evolution of magnetized relativistic sheared plasma flows

摘要

We explore, via analytical and numerical methods, the Kelvin-Helmholtz (KH) instability in relativistic magnetizednplasmas, with applications to astrophysical jets.We solve the single-fluid relativistic magnetohydrodynamicn(RMHD) equations in conservative form using a scheme which is fourth order in space and time. To recover thenprimitive RMHD variables, we use a highly accurate, rapidly convergent algorithm which improves upon suchnschemes as the Newton-Raphson method. Although the exact RMHD equations are marginally stable, numericalndiscretization renders them unstable.We include numerical viscosity to restore numerical stability. In relativisticnflows, diffusion can lead to a mathematical anomaly associated with frame transformations. However, in ournKH studies, we remain in the rest frame of the system, and therefore do not encounter this anomaly. We usena two-dimensional slab geometry with periodic boundary conditions in both directions. The initial unperturbednvelocity peaks along the central axis and vanishes asymptotically at the transverse boundaries. Remainingnunperturbed quantities are uniform, with a flow-aligned unperturbed magnetic field. The early evolution in thennonlinear regime corresponds to the formation of counter-rotating vortices, connected by filaments, which persistnin the absence of a magnetic field. A magnetic field inhibits the vortices through a series of stages, namely,nfield amplification, vortex disruption, turbulent breakdown, and an approach to a flow-aligned equilibriumnconfiguration. Similar stages have been discussed in MHD literature. We examine how and to what extent thesenstages manifest in RMHD for a set of representative field strengths. To characterize field strength, we define anrelativistic extension of the Alfv´enic Mach number MA. We observe close complementarity between flow andnmagnetic field behavior. Weaker fields exhibit more vortex rotation, magnetic reconnection, jet broadening, andnintermediate turbulence. Sufficiently strong fields (MA < 6) completely suppress vortex formation. Maximumnjet deceleration, and viscous dissipation, occur for intermediate vortex-disruptive fields, while electromagneticnenergy is maximized for the strongest fields which allow vortex formation. Highly relativistic flows destabilizenthe system, supporting modes with near-maximum growth at smaller wavelengths than the shear width of thenvelocity. This helps to explain early numerical breakdown of highly relativistic simulations using numericalnviscosity, a long-standing problem.While magnetic fields generally stabilize the system, we have identified manynfeatures of the complex and turbulent reorganization that occur for sufficiently weak fields in RMHD flows, andnhave described the transition from disruptive to stabilizing fields at MA ≈ 6. Our results are qualitatively similarnto observations of numerous jets, including M87, whose knots may exhibit vortex-like behavior. Furthermore, innboth the linear and nonlinear analyses, we have successfully unified the HD, MHD, RHD, and RMHD regimes.