Probability density functions in steady-state Burgers turbulence

概要

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Probability density functions (PDFs) for steady-state Burgers turbulence supported by white-in-time random forcing at low wave numbers are studied by direct numerical simulation and compared to theoretical predictions. The velocity PDFs decay slightly faster than a Gaussian at large amplitudes. The putative power law exponent α of the PDF Q(ξ)∝|ξ|-α of velocity gradient ξ is examined at large Reynolds number and found to be approximately 3 or slightly greater. The tail of Q(ξ) behaves like |Rξ|-1exp(-c(|ξ|/Rξf)θ1) at large negative ξ, where ξf is a forcing parameter. The exponent θ1 is near unity, which is smaller than predicted by theory. It decreases slowly with the Reynolds number R up to R = 14000. The central parts of the PDFs of higher velocity space derivatives are found to be cusp-like, and the cusp exponents are measured. The PDF tails are stretched exponentials.
American Institute of Physicsの論文