Open AccessTransition of fluctuations from Gaussian state to turbulent state
Author(s) -
Toshiyuki Gotoh,
Jingyuan Yang
Publication year - 2022
Publication title -
philosophical transactions - royal society. mathematical, physical and engineering sciences/philosophical transactions - royal society. mathematical, physical and engineering sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.074
H-Index - 169
eISSN - 1471-2962
pISSN - 1364-503X
DOI - 10.1098/rsta.2021.0097
Subject(s) - enstrophy , dissipation , physics , turbulence , probability density function , scalar (mathematics) , isotropy , reynolds number , scaling , statistical physics , gaussian , compressibility , classical mechanics , mathematics , statistics , mechanics , quantum mechanics , vorticity , geometry , vortex
Variation of the statistical properties of an incompressible velocity, passive vector and passive scalar in isotropic turbulence was studied using direct numerical simulation. The structure functions of the gradients, and the moments of the dissipation rates, began to increase at aboutR λ ∼ 2 from the Gaussian state and grew rapidly atR λ > 20 in the turbulent state. A contour map of the probability density functions (PDFs) indicated that PDF expansion of the gradients of the passive vector and passive scalar begins at aroundR λ ≈ 4 , whereas that of the longitudinal velocity gradient PDF is more gradual. The left tails of the dissipation rate PDF were found to follow a power law with an exponent of 3/2 for the incompressible velocity and passive vector dissipation rates, and 1/2 for the scalar dissipation rate and the enstrophy; they remained constant for all Reynolds numbers, indicating the universality of the left tail. The analytical PDFs of the dissipation rates and enstrophy of the Gaussian state were obtained and found to be the Gamma distribution. It was shown that the number of terms contributing to the dissipation rates and the enstrophy determines the decay rates of the two PDFs for low to moderate amplitudes.This article is part of the theme issue ‘Scaling the turbulence edifice (part 1)’.