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Turbulence Energetics in an Inclined Interface Richtmyer-Meshkov Instability

Akshay Subramaniam
Department of Aeronautics & Astronautics, Stanford University 496 Lomita Mall, Stanford, CA, USA 94305

Sanjiva K. Lele
Dept. of Aeronautics & Astronautics, and Dept. of Mechanichal Engineering Stanford University, Stanford, CA 94305-4035, USA


The interaction of a Mach 1.55 shockwave with a nominally inclined interface between N2 and CO2 is considered. Unlike the classical Richtmyer-Meshkov problem, the interface evolution is nonlinear from early time and large highly correlated vortical structures are observed even after reshock. Simulations target the experiment of McFarland et al. (2014). Simulations are performed using highorder spectral-like numerics (Lele, 1992). Results from multiple grid resolutions up to 4 billion grid points establish grid insensitivity of important physical quantities. Comparisons to the experiments show that the simulations adequately capture the physics of the problem. Analysis of the simulation data based on variable density turbulence equations in the Favre averaged and filtered form is presented. Statistics of unclosed terms in the averaged and filtered variable density equations are presented with a focus on the energy dynamics. It is observed that the inhomogeniety in the problem results in a non-monotonic return to isotropy of the Reynolds stresses post reshock and that compressibility effects are strong long after reshock due to large scale pressure-dilatation correlation. Binning the kinetic energy into logarithmically spaced bins in wavenumber space shows a k−2 scaling of the energy spectrum post reshock instead of the standard k−5/3 power law.