Abstract
The computational prediction of nonlinear interactive instabilities in three-dimensional boundary layers is obtained for a warm dense plasma boundary layer environment. The method is applied to the Richtmyer–Meshkov flow over the rippled surface of a laser-driven warm dense plasma experiment. Coupled, nonlinear spectral velocity equations of Lorenz form are solved with the mean boundary-layer velocity gradients as input control parameters. The nonlinear time series solutions indicate that after an induction period, a sharp instability occurs in the solutions. The power spectral density yields the available kinetic energy dissipation rates within the instability. The application of the singular value decomposition technique to the nonlinear time series solution yields empirical entropies. Empirical entropic indices are then obtained from these entropies. The intermittency exponents obtained from the entropic indices thus allow the computation of the entropy generation through the deterministic structure to the final dissipation of the initial fluctuating kinetic energy into background thermal energy, representing the resulting entropy increase.
Highlights
In this article, we present the results of an exploratory computational study of a possible instability in the Richtmyer–Meshkov flow over a surface deflection in a warm dense plasma environment
From the experimental results presented by Harding [3], we assume that the Richtmyer–Meshkov flow downstream of the strong oblique shock wave forms a laminar boundary layer over the foam substrate surface
A corresponding effect occurs between the boundary layer produced in the x-z plane and a crossflow velocity produced by the boundary layer flow in the x-y plane, producing a second deterministic structure in the corner three-dimensional boundary layer flow
Summary
We present the results of an exploratory computational study of a possible instability in the Richtmyer–Meshkov flow over a surface deflection in a warm dense plasma environment. Additional laser facilities have been implemented to support this effort and are capable of providing the warm dense matter required to simulate the environment found in supernova plasma [2] Results obtained from these facilities have confirmed the existence of the Rayleigh–Taylor instability (buoyancy effect between two adjacent layers), the Kelvin–Helmholtz instability (the effect of shear between adjacent layers), and the Richtmyer–Meshkov instability (induced parallel flow due to surface ripples) [2]. These equations are Fourier transformed into a set of deterministic equations (Hellberg and Orszag [15], Isaacson [16], Manneville [17]) from which the time-dependent behavior of the both the Fourier components of the wave number vectors and the Fourier components of the fluctuating velocity wave vectors are obtained. The article closes with a discussion of the results and final conclusions
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