Scaling of back scatter in a Richtmyer-Meshkov mixing layer

High resolution numerical simulations of the Richtmyer-Meshkov instability are used to test the scaling of fluctuations. Mesh resolutions as high as 2048x2048x1920 are employed. Mass weighted Gaussian filters of varying widths are applied to the flow results, which decomposes the flow fields into two components : resolved and unresolved by the filter. Reynolds stresses are measured for each filter. A spatially local form of the energy flux is defined and calculated for each filter width. Both forward and back transfer between resolved and unresolved scales are observed. Very little backscatter is seen for filter widths near the energy containing range, while the fractional backscatter systematically increases with decreasing filter width. The relevance to sub-grid scale models of turbulence is discussed. Work performed under the auspices of the USDOE by Lawrence Livermore National Laboratory under contract No. W-7405-ENG-48. We thank T. A. Peyser and O. Schilling for helpful discussions on which experiment to model.