On the Kelvin-Helmholtz instability with smooth initial conditions -- Linear theory and simulations

Abstract

The Kelvin-Helmholtz instability (KHI) is a standard test of hydrodynamic and magnetohydrodynamic (MHD) simulation codes and finds many applications in astrophysics. The classic linear theory considers a discontinuity in density and velocity at the interface of two fluids. However, for numerical simulations of the KHI such initial conditions do not yield converged results even at the linear stage of the instability. Instead, smooth profiles of velocity and density are required for convergence. This renders analytical theory to be only approximately valid and hinders quantitative comparisons between the classical theory and simulations. In this paper we derive a linear theory for the KHI with smooth profiles and illustrate code testing with the MHD code Athena. We provide the linear solution for the KHI with smooth initial conditions in three different limits: inviscid hydrodynamics, ideal MHD and Braginskii-MHD. These linear solutions are obtained numerically with the framework Psecas (Pseudo-Spectral Eigenvalue Calculator with an Automated Solver), which generates and solves numerical eigenvalue problems using an equation-parser and pseudo-spectral methods. The Athena simulations are carried out on a periodic, Cartesian domain which is useful for code testing purposes. Using Psecas and analytic theory, we outline the differences between this artificial numerical setup and the KHI on an infinite Cartesian domain and the KHI in cylindrical geometry. We discuss several astrophysical applications, such as cold flows in galaxy formation and cold fronts in galaxy cluster mergers. Psecas, and the linear solutions used for code testing, are publicly available and can be downloaded from the web.

arXiv comment18 pages, 10 figures, accepted for publication in MNRAS. Code available at http://github.com/tberlok/psecas

References in corpus (46)

• E pur si muove: Galiliean-invariant cosmological hydrodynamical simulations on a moving mesh
• Astrophysics Source Code Library
• Athena: A New Code for Astrophysical MHD
• Shocks and cold fronts in galaxy clusters
• Fundamental differences between SPH and grid methods
• An Unsplit Godunov Method for Ideal MHD via Constrained Transport
• Improving the convergence properties of the moving-mesh code AREPO
• Simulations of magnetic fields in isolated disk galaxies
• An Unsplit Godunov Method for Ideal MHD via Constrained Transport in Three Dimensions
• Magnetohydrodynamics on an unstructured moving grid
• Draping of Cluster Magnetic Fields over Bullets and Bubbles -- Morphology and Dynamic Effects
• Plasma instabilities and magnetic-field growth in clusters of galaxies
• Stability, Instability, and "Backwards'' Transport in Accretion Disks"
• Buoyancy Instabilities in Weakly Magnetized Low Collisionality Plasmas
• Chandra estimate of the magnetic field strength near the cold front in A3667
• Convective and Rotational Stability of a Dilute Plasma
• A Well-Posed Kelvin-Helmholtz Instability Test and Comparison
• The MHD Kelvin-Helmholtz Instability: A Two-Dimensional Numerical Study
• Numerical Magnetohydrodynamics in Astrophysics: Algorithm and Tests for Multi-Dimensional Flow
• Simulations of radiative turbulent mixing layers
• A Validated Nonlinear Kelvin-Helmholtz Benchmark for Numerical Hydrodynamics
• Computational Eulerian Hydrodynamics and Galilean Invariance
• Cluster mergers, core oscillations, and cold fronts
• Cold Fronts: Probes of Plasma Astrophysics in Galaxy Clusters
• On the Saturation of the Magnetorotational Instability via Parasitic Modes
• Instability of Supersonic Cold Streams Feeding Galaxies I: Linear Kelvin-Helmholtz Instability with Body Modes
• Angular Momentum Transport in Protoplanetary and Black-Hole Accretion Disks: The Role of Parasitic Modes in the Saturation of MHD Turbulence
• The Kelvin-Helmholtz Instability at CME-Boundaries in the Solar Corona: Observations and 2.5D MHD Simulations
• The Effect of Anisotropic Viscosity on Cold Fronts in Galaxy Clusters
• Cold gas in cluster cores: Global stability analysis and non-linear simulations of thermal instability
• Instability of Supersonic Cold Streams Feeding Galaxies III: Kelvin-Helmholtz Instability in Three Dimensions
• Viscous Kelvin-Helmholtz instabilities in highly ionised plasmas
• Termination of the magnetorotational instability via parasitic instabilities in core-collapse supernovae
• A stringent limit on the amplitude of Alfvénic perturbations in high-beta low-collisionality plasmas
• Self-organisation in protoplanetary disks: global, non-stratified Hall-MHD simulations
• Instability of Supersonic Cold Streams Feeding Galaxies II. Nonlinear Evolution of Surface and Body Modes of Kelvin-Helmholtz Instability
• The Likely Orbital Period of the Ultracompact Low-Mass X-Ray Binary 2S 0918-549
• Dust segregation in Hall-dominated turbulent protoplanetary disks
• The Kelvin-Helmholtz instability in Orion: a source of turbulence and chemical mixing
• Importance of resolving the spectral support of beam-plasma instabilities in simulations
• Stability of cold fronts in clusters: is magnetic field necessary?
• Linear analysis of the vertical shear instability: outstanding issues and improved solutions (Research Note)
• The HBI in a quasi-global model of the intracluster medium
• On the Anisotropic Nature of MRI-Driven Turbulence in Astrophysical Disks
• On Helium Mixing in Quasi-global Simulations of the Intracluster Medium
• Investigating the Optical Counterpart Candidates of Four INTEGRAL Sources localized with Chandra

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