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.
It is suggested that the wavelike character of the recently discovered 2.7-kiloparsec spatially and kinematically coherent complex of interstellar clouds in the solar neighborhood--the Radcliffe Wave--may be the result of a Kelvin-Helmholtz instability arising at the interface between the Galactic disk and non-corotating halo.
There has been interest in recent years to assess the ability of astrophysical hydrodynamics codes to correctly model the Kelvin-Helmholtz instability. Smoothed particle hydrodynamics (SPH), in particular, has received significant attention, though there has yet to be a clear demonstration that SPH yields converged solutions that are in agreement with other methods. We have performed SPH simulations of the Kelvin-Helmholtz instability using the test problem put forward by Lecoanet et al (2016). We demonstrate that the SPH solutions converge to the reference solution in both the linear and non-…
Continued star formation over the lifetime of a galaxy suggests that low metalicity gas is steadily flowing in from the circumgalactic medium. Also, cosmological simulations of large-scale structure formation imply that gas is accreted onto galaxies from the halo inside which they formed. Direct observations are difficult, but in recent years observational indications of gas inflows from a circumgalactic medium were obtained. Here we suggest an indirect observational probe: looking for large-scale (exceeding few kpc) turbulence caused by the accretion. As a specific example we consider an accr…
We study Kelvin-Helmholtz (KH) instability at the interface of a disc and corona system by doing a linear perturbation analysis. The disc is assumed to be thin, however, the corona is considered to be nearly quasispherical because of its high temperature. Under these circumstances, the interface is subject to the KH instability for a given set of the input parameters. Growth rates of the KH unstable modes are calculated for a wide range of the input parameters. We show that for a certain range of the perturbations, the unstable KH perturbations are growing with time scales comparable to the in…
Numerical simulations for the non-linear development of Kelvin-Helmholtz instability in two different density layers have been performed with the particle-based method (Godunov SPH) developed by Inutsuka (2002). The Godunov SPH can describe the Kelvin-Helmholtz instability even with a high density contrast, while the standard SPH shows the absence of the instability across a density gradient (Agertz et al. 2007). The interaction of a dense blob with a hot ambient medium has been performed also. The Godunov SPH describes the formation and evolution of the fingers due to the combinations of Rayl…
The Kelvin-Helmholtz instability is well known to be capable of converting well-ordered flows into more disordered, even turbulent, flows. As such it could represent a path by which the energy in, for example, bowshocks from stellar jets could be converted into turbulent energy thereby driving molecular cloud turbulence. We present the results of a suite of fully multifluid magnetohydrodynamic simulations of this instability using the HYDRA code. We investigate the behaviour of the instability in a Hall dominated and an ambipolar diffusion dominated plasma as might be expected in certain regio…
The purpose of this study is to analyze the dynamical role of a radiation field on the growth rate of the unstable Kelvin - Helmholtz (KH) perturbations. As a first step toward this purpose, the analyze is done in a general way, irrespective of applying the model to a specific astronomical system. The transition zone between the two layers of the fluid is ignored. Then, we perform a linear analysis and by imposing suitable boundary conditions and considering a radiation field, we obtain appropriate dispersion relation. Unstable modes are studied by solving the dispersion equation numerically, …
Observations of galaxies and models of accreting systems point to the occurrence of counter-rotating discs where the inner part of the disc ($r<r_0$) is co-rotating and the outer part is counter-rotating. This work analyzes the linear stability of radially separated co- and counter-rotating thin discs. The strong instability found is the supersonic Kelvin-Helmholtz instability. The growth rates are of the order of or larger than the angular rotation rate at the interface. The instability is absent if there is no vertical dependence of the perturbation. That is, the instability is essentially t…
Over the last few years it became clear that turbulent magnetic reconnection and magnetized turbulence are inseparable. It was not only shown that reconnection is responsible for violating the frozen-in condition in turbulence, but also that stochastic reconnection in 3D generates turbulence by itself. The actual mechanism responsible for this driving is still unknown. Processes such tearing mode or Kelvin-Helmholtz, among other plasma instabilities, could generate turbulence from irregular current sheets. We address the nature of driving mechanism for this process and consider a relative role…
We perform simulations of the Kelvin-Helmholtz instability using smoothed particle hydrodynamics (SPH). The instability is studied both in the linear and strongly non-linear regimes. The smooth, well-posed initial conditions of Lecoanet et al. (2016) are used, along with an explicit Navier-Stokes viscosity and thermal conductivity to enforce the evolution in the non-linear regime. We demonstrate convergence to the reference solution using SPH. The evolution of the vortex structures and the degree of mixing, as measured by a passive scalar `colour' field, match the reference solution. Tests wit…
We present a study of the Kelvin-Helmholtz instability in a weakly ionised, multifluid MHD plasma with parameters matching those of a typical molecular cloud. The instability is capable of transforming well-ordered flows into disordered flows. As a result, it may be able to convert the energy found in, for example, bowshocks from stellar jets into the turbulent energy found in molecular clouds. As these clouds are weakly ionised, the ideal magnetohydrodynamic approximation does not apply at scales of around a tenth of a parsec or less. This paper extends the work of Jones & Downes (2011) on th…
The origin of striations aligned along the local magnetic field direction in the translucent envelope of the Taurus molecular cloud is examined with new observations of 12CO and 13CO J=2-1 emission obtained with the 10~m submillimeter telescope of the Arizona Radio Observatory. These data identify a periodic pattern of excess blue and redshifted emission that is responsible for the striations. For both 12CO and 13CO, spatial variations of the J=2-1 to J=1-0 line ratio are small and are not spatially correlated with the striation locations. A medium comprised of unresolved CO emitting substruct…
The presence of dust grains profoundly affects the diffusion of the magnetic field in molecular clouds. When the electrons and ions are well coupled to the magnetic field and charged grains are only indirectly coupled, emergent Hall diffusion may dominate over all the other non ideal magnetohydrodynamic (MHD) effects in a partially ionized dusty cloud. The low frequency, long wavelength (0.01 t0 1 pc) dispersive MHD waves will propagate in such a medium with the polarization of the waves determined by the dust charge density or the dust size distribution. In the presence of shear flows, these …
In this paper we investigate whether Smoothed Particle Hydrodynamics (SPH), equipped with artificial conductivity, is able to capture the physics of density/energy discontinuities in the case of the so-called shearing layers test, a test for examining Kelvin-Helmholtz (KH) instabilities. We can trace back each failure of SPH to show KH rolls to two causes: i) shock waves travelling in the simulation box and ii) particle clumping, or more generally, particle noise. The probable cause of shock waves is the Local Mixing Instability (LMI), previously identified in the literature. Particle noise on…
Deep observations of nearby galaxy clusters with Chandra have revealed concave 'bay' structures in a number of systems (Perseus, Centaurus and Abell 1795), which have similar X-ray and radio properties. These bays have all the properties of cold fronts, where the temperature rises and density falls sharply, but are concave rather than convex. By comparing to simulations of gas sloshing, we find that the bay in the Perseus cluster bears a striking resemblance in its size, location and thermal structure, to a giant ($\approx$50 kpc) roll resulting from Kelvin-Helmholtz instabilities. If true, th…
Hydrodynamical instabilities are believed to power some of the small scale (0.1-10 pc) turbulence and chemical mixing in the interstellar medium. Identifying such instabilities has always been difficult but recent observations of a wavelike structure (the Ripples) in the Orion nebula have been interpreted as a signature of the Kelvin-Helmholtz instability (KHI), occurring at the interface between the HII region and the molecular cloud. However, this has not been verified theoretically. In this letter, we investigate theoretically the stability of this interface using observational constraints …
As part of our long-term campaign to understand how cold streams feed massive galaxies at high redshift, we study the Kelvin-Helmholtz instability (KHI) of a supersonic, cold, dense gas stream as it penetrates through a hot, dilute circumgalactic medium (CGM). A linear analysis (Paper I) showed that, for realistic conditions, KHI may produce nonlinear perturbations to the stream during infall. Therefore, we proceed here to study the nonlinear stage of KHI, still limited to a two-dimensional slab with no radiative cooling or gravity. Using analytic models and numerical simulations, we examine s…
Cosmic filaments play a crucial role in galaxy evolution transporting gas from the intergalactic medium into galaxies. However, little is known about the efficiency of this process and whether the gas is accreted in a homogenous or clumpy way. Recent observations suggest the presence of broad gas density distributions in the circumgalactic medium which could be related to the accretion of filaments. By means of high-resolution hydrodynamical simulations, we explore here the evolution of cold accreting filaments flowing through the hot circumgalactic medium (CGM) of high-z galaxies. In particul…
The nonlinear magnetic Kelvin-Helmholtz instability (KHi), and the turbulence it creates, appears in many astrophysical systems. This includes those systems where the local plasma conditions are such that the plasma is not fully ionised, for example in the lower solar atmosphere and molecular clouds. In a partially ionised system, the fluids couple via collisions which occur at characteristic frequencies, therefore neutral and plasma species become decoupled for sufficiently high-frequency dynamics. Here we present high-resolution 2D two-fluid simulations of the nonlinear KHi for a system that…
