Entropy Generation through a Deterministic Boundary-Layer Structure in Warm Dense Plasma

Abstract

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.

Entropy Generation through Deterministic Spiral Structures in Corner Flows with Sidewall Surface Mass Injection

“…The solution of the steady-state boundary-layer equations that provides these control parameters is dependent on the particular value of the kinematic viscosity applied in the calculations. We have found that only a narrow range of kinematic viscosities yields the prediction of ordered structures from the computational procedure (see e.g., [1][2][3][4][5]). The range of appropriate values of kinematic viscosities has not been delineated and remains as work to be done.…”

“…Singular value decomposition of the time series solutions provides empirical entropies for these deterministic structures. The empirical entropic indices of the Tsallis form extracted from the empirical entropies using Equation (5) have been used to obtain the intermittency exponents for the ordered structures. We heuristically apply a relationship, found by Arimitsu and Arimitsu [22], connecting the entropic index of Tsallis to the intermittency exponent, ζ j .…”

“…The fraction of dissipation kinetic energy within each empirical mode of the power spectral energy distribution is denoted as ξ j . Then the total rate of dissipation of the available fluctuating kinetic energy for the stream wise, normal and span wise velocity components is the summation, over the empirical modes, j, of the product of the kinetic energy fraction of each mode times the intermittency exponent for that mode, ζ j [5].…”

Entropy Generation through Deterministic Spiral Structures in a Corner Boundary-Layer Flow

“…The rate of dissipation of kinetic energy within each empirical mode of the power spectral energy distribution is denoted as ξj. Then the total rate of dissipation of the available fluctuating kinetic energy for the normal and span wise velocity components is the summation, over the empirical modes, j, of the product of the kinetic energy fraction of each mode times the intermittency exponent for that mode, ζj [25].…”

“…The boundary layer mean velocity may be written, from Equation (11), as u = uef'. The expression for the entropy generation rate through the deterministic spiral structures may then be written as [25]:…”