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- W3103485669 abstract "The probabilistic approach to turbulence is applied to investigate density fluctuations in supersonic turbulence. We derive kinetic equations for the probability distribution function (PDF) of the logarithm of the density field, $s$, in compressible turbulence in two forms: a first-order partial differential equation involving the average divergence conditioned on the flow density, $langle nabla cdot {bs u} | srangle$, and a Fokker-Planck equation with the drift and diffusion coefficients equal to $-langle {bs u} cdot nabla s | srangle$ and $langle {bs u} cdot nabla s | srangle$, respectively. Assuming statistical homogeneity only, the detailed balance at steady state leads to two exact results, $langle nabla cdot {bs u} | s rangle =0$, and $langle {bs u} cdot nabla s | srangle=0$. The former indicates a balance of the flow divergence over all expanding and contracting regions at each given density. The exact results provide an objective criterion to judge the accuracy of numerical codes with respect to the density statistics in supersonic turbulence. We also present a method to estimate the effective numerical diffusion as a function of the flow density and discuss its effects on the shape of the density PDF." @default.
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- W3103485669 date "2018-10-12" @default.
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- W3103485669 title "Detailed Balance and Exact Results for Density Fluctuations in Supersonic Turbulence" @default.
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- W3103485669 doi "https://doi.org/10.3847/2041-8213/aae57c" @default.
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