Journal
ASTROPHYSICAL JOURNAL LETTERS
Volume 866, Issue 2, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.3847/2041-8213/aae57c
Keywords
ISM: kinematics and dynamics; stars: formation; turbulence
Categories
Funding
- Youth Program of the Thousand Talents Plan in China
- Spanish MINECO [AYA2017-88754-P]
- Danish Council for Independent Research (DFF) [1323-00199B]
- Danish National Research Foundation [DNRF97]
- Villum Fonden [VKR023406]
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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, , and a Fokker-Planck equation with the drift and diffusion coefficients equal to -< u . del s vertical bar s > and < u . del s vertical bar s >, respectively. Assuming statistical homogeneity only, the detailed balance at steady state leads to two exact results, = 0, and < u . del s vertical bar s > = 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.
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