The Dynamics of Rayleigh-Taylor Stable and Unstable Contact Discontinuities with Anisotropic Thermal Conduction

We study the effects of anisotropic thermal conduction along magnetic field lines on an accelerated contact discontinuity in a weakly collisional plasma. We first perform a linear stability analysis similar to that used to derive the Rayleigh-Taylor instability (RTI) dispersion relation. We find that anisotropic conduction is only important for compressible modes, as incompressible modes are isothermal. Modes grow faster in the presence of anisotropic conduction, but growth rates do not change by more than a factor of order unity. We next run fully non-linear numerical simulations of a contact discontinuity with anisotropic conduction. The non-linear evolution can be thought of as a superposition of three physical effects: temperature diffusion due to vertical conduction, the RTI, and the heat flux driven buoyancy instability (HBI). In simulations with RTI-stable contact discontinuities, the temperature discontinuity spreads due to vertical heat conduction. This occurs even for initially horizontal magnetic fields due to the initial vertical velocity perturbation and numerical mixing across the interface. The HBI slows this temperature diffusion by reorienting initially vertical magnetic field lines to a more horizontal geometry. In simulations with RTI-unstable contact discontinuities, the dynamics are initially governed by temperature diffusion, but the RTI becomes increasingly important at late times. We discuss the possible application of these results to supernova remnants, solar prominences, and cold fronts in galaxy clusters.Comment: 18 pages, 15 figures, submitted to MNRA

Nonlinear Evolution of the Magnetohydrodynamic Rayleigh-Taylor Instability

We study the nonlinear evolution of the magnetic Rayleigh-Taylor instability using three-dimensional MHD simulations. We consider the idealized case of two inviscid, perfectly conducting fluids of constant density separated by a contact discontinuity perpendicular to the effective gravity g, with a uniform magnetic field B parallel to the interface. Modes parallel to the field with wavelengths smaller than l_c = [B B/(d_h - d_l) g] are suppressed (where d_h and d_l are the densities of the heavy and light fluids respectively), whereas modes perpendicular to B are unaffected. We study strong fields with l_c varying between 0.01 and 0.36 of the horizontal extent of the computational domain. Even a weak field produces tension forces on small scales that are significant enough to reduce shear (as measured by the distribution of the amplitude of vorticity), which in turn reduces the mixing between fluids, and increases the rate at which bubbles and finger are displaced from the interface compared to the purely hydrodynamic case. For strong fields, the highly anisotropic nature of unstable modes produces ropes and filaments. However, at late time flow along field lines produces large scale bubbles. The kinetic and magnetic energies transverse to gravity remain in rough equipartition and increase as t^4 at early times. The growth deviates from this form once the magnetic energy in the vertical field becomes larger than the energy in the initial field. We comment on the implications of our results to Z-pinch experiments, and a variety of astrophysical systems.Comment: 25 pages, accepted by Physics of Fluids, online version of journal has high resolution figure

The Magnetic Rayleigh-Taylor Instability in Three Dimensions

We study the magnetic Rayleigh-Taylor instability in three dimensions, with focus on the nonlinear structure and evolution that results from different initial field configurations. We study strong fields in the sense that the critical wavelength l_c at which perturbations along the field are stable is a large fraction of the size of the computational domain. We consider magnetic fields which are initially parallel to the interface, but have a variety of configurations, including uniform everywhere, uniform in the light fluid only, and fields which change direction at the interface. Strong magnetic fields do not suppress instability, in fact by inhibiting secondary shear instabilities, they reduce mixing between the heavy and light fluid, and cause the rate of growth of bubbles and fingers to increase in comparison to hydrodynamics. Fields parallel to, but whose direction changes at, the interface produce long, isolated fingers separated by the critical wavelength l_c, which may be relevant to the morphology of the optical filaments in the Crab nebula.Comment: 14 pages, 9 pages, accepted by Ap

Effect of Electromigration on Onset of Morphological Instability of a Nanowire

Solid cylindrical nanowires are vulnerable to a Rayleigh-Plateau-type morphological instability. The instability results in a wire breakup, followed by formation of a chain array of spherical nanoparticles. In this paper, a base model of a morphological instability of a nanowire on a substrate in the applied electric field directed along a nanowire axis is considered. Exact analytical solution is obtained for 90 degrees contact angle and, assuming axisymmetric perturbations, for a free-standing wire. The latter solution extends the 1965 result by Nichols and Mullins without electromigration effect (F.A. Nichols and W.W. Mullins, Trans. Metall. Soc. AIME 233, 1840-1848 (1965)). For general contact angles the neutral stability is determined numerically. It is shown that a stronger applied electric field (a stronger current) results in a larger instability growth rate and a decrease of the most dangerous unstable wavelength; in experiment, the latter is expected to yield more dense chain array of nanoparticles. Also it is noted that a wire crystallographic orientation on a substrate has larger impact on stability in a stronger electric field and that a simple switching of the polarity of electrical contacts, i.e. the reversal of the direction of the applied electric field, may suppress the instability development and thus a wire breakup would be prevented. A critical value of the electric field that is required for such wire stabilization is obtained

Large-eddy simulation and multiscale modelling of a Richtmyer–Meshkov instability with reshock

Large-eddy simulations of the Richtmyer–Meshkov instability with reshock are pre- sented and the results are compared with experiments. Several configurations of shocks initially travelling from light (air) to heavy (sulfur hexafluoride, SF6) have been simulated to match previous experiments and good agreement is found in the growth rates of the turbulent mixing zone (TMZ). The stretched-vortex subgrid model used in this study allows for subgrid continuation modelling, where statistics of the unresolved scales of the flow are estimated. In particular, this multiscale modelling allows the anisotropy of the flow to be extended to the dissipation scale, eta, and estimates to be formed for the subgrid probability density function of the mixture fraction of air/SF6 based on the subgrid variance, including the effect of Schmidt number