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Degeneracy of velocity strain-rate tensor statistics in random isotropic incompressible flows

A. V. Kopyev*

  • P.N. Lebedev Physical Institute of the Russian Academy of Sciences, 53 Leninskiy Prospekt, 119991, Moscow, Russia

  • *kopyev@lpi.ru
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Phys. Rev. Fluids 3, 024603 – Published 13 February, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.024603

Abstract

The article considers the strain-rate tensor distribution in various isotropically distributed incompressible flows. By means of a fortunate choice of variables, a strong degeneracy in the probability distribution of strain-rate tensor characteristics is found in numerical simulations of isotropic turbulence. This allows us to reduce the probability density function (PDF) of the strain-rate tensor to a function of one variable. Also it appears that for those particular parameters that reflect the ratio of different eigenvalues of the strain tensor (s and β parameters), the shapes of their probability distributions are universal and do not depend on the specific shape of distribution. Furthermore, it is also shown analytically that for all time-reversible statistical isotropic flows the probability distribution of s is uniform, which generalizes previous numerical calculations.

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Phys. Rev. Fluids 3, 024603– Published 13 February, 2018
  • Received 2 August 2017
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