Hypervelocity Richtmyer–Meshkov instability

The Richtmyer-Meshkov instability is numerically investigated for strong shocks, i.e., for hypervelocity cases. To model the interaction of the flow with non-equilibrium chemical effects typical of high-enthalpy flows, the Lighthill-Freeman ideal dissociating gas model is employed. Richtmyer's linear theory and the impulse model are extended to include equilibrium dissociation chemistry. Numerical simulations of the compressible Euler equations indicate no period of linear growth even for amplitude to wavelength ratios as small as one percent. For large Atwood numbers, dissociation causes significant changes in density and temperature, but the change in growth of the perturbations is small. A Mach number scaling for strong shocks is presented which holds for frozen chemistry at high Mach numbers. A local analysis is used to determine the initial baroclinic circulation generation for interfaces corresponding to both positive and negative Atwood ratios

On initial-value and self-similar solutions of the compressible Euler equations

We examine numerically the issue of convergence for initial-value solutions and similarity solutions of the compressible Euler equations in two dimensions in the presence of vortex sheets (slip lines). We consider the problem of a normal shock wave impacting an inclined density discontinuity in the presence of a solid boundary. Two solution techniques are examined: the first solves the Euler equations by a Godunov method as an initial-value problem and the second as a boundary value problem, after invoking self-similarity. Our results indicate nonconvergence of the initial-value calculation at fixed time, with increasing spatial-temporal resolution. The similarity solution appears to converge to the weak 'zero-temperature' solution of the Euler equations in the presence of the slip line. Some speculations on the geometric character of solutions of the initial-value problem are presented

The Richtmyer–Meshkov instability in magnetohydrodynamics

In ideal magnetohydrodynamics (MHD), the Richtmyer–Meshkov instability can be suppressed by the presence of a magnetic field. The interface still undergoes some growth, but this is bounded for a finite magnetic field. A model for this flow has been developed by considering the stability of an impulsively accelerated, sinusoidally perturbed density interface in the presence of a magnetic field that is parallel to the acceleration. This was accomplished by analytically solving the linearized initial value problem in the framework of ideal incompressible MHD. To assess the performance of the model, its predictions are compared to results obtained from numerical simulation of impulse driven linearized, shock driven linearized, and nonlinear compressible MHD for a variety of cases. It is shown that the analytical linear model collapses the data from the simulations well. The predicted interface behavior well approximates that seen in compressible linearized simulations when the shock strength, magnetic field strength, and perturbation amplitude are small. For such cases, the agreement with interface behavior that occurs in nonlinear simulations is also reasonable. The effects of increasing shock strength, magnetic field strength, and perturbation amplitude on both the flow and the performance of the model are investigated. This results in a detailed exposition of the features and behavior of the MHD Richtmyer–Meshkov flow. For strong shocks, large initial perturbation amplitudes, and strong magnetic fields, the linear model may give a rough estimate of the interface behavior, but it is not quantitatively accurate. In all cases examined the accuracy of the model is quantified and the flow physics underlying any discrepancies is examine

Energy transfers and magnetic energy growth in small-scale dynamo

In this letter we investigate the dynamics of magnetic energy growth in small-scale dynamo by studying energy transfers, mainly energy fluxes and shell-to-shell energy transfers. We perform dynamo simulations for magnetic Prandtl number $\mathrm{Pm}=20$ on $1024^3$ grid using pseudospectral method. We demonstrate that the magnetic energy growth is caused by nonlocal energy transfers from the large-scale or forcing-scale velocity field to small-scale magnetic field. The peak of these energy transfers move towards lower wavenumbers as dynamo evolves, which is the reason why the integral scale of the magnetic field increases with time. The energy transfers $U2U$ (velocity to velocity) and $B2B$ (magnetic to magnetic) are forward and local.Comment: 6 pages, 8 figure