Crossover from high to low Reynolds number turbulence

Detlef Lohse

doi:10.1103/PhysRevLett.73.3223

paper

Crossover from high to low Reynolds number turbulence

arXiv:chao-dyn/9401005 · doi:10.1103/PhysRevLett.73.3223

Abstract

The Taylor-Reynolds and Reynolds number ( $R e_{λ}$ and $R e$ ) dependence of the dimensionless energy dissipation rate $\ceps =\eps L / \u1rms^3$ is derived for statistically stationary isotropic turbulence, employing the results of a variable range mean field theory. Here, $\eps$ is the energy dissipation rate, $L$ is the (fixed) outer length scale, and $1 ˘ r m s$ a rms velocity component. Our fit-parameter free results for $\ceps (Re_λ)$ and also for $R e_{λ} (R e)$ are in good agreement with experimental data. Using the $R e$ -dependence of $\ceps$ we account for the time dependence of the mean vorticity $ω (t)$ for decaying isotropic turbulence, which was recently experimentally examined [M.\ Smith, R.\ J.\ Donelly, N.\ Goldenfeld, and W.\ F.\ Vinen, Phys.\ Rev.\ Lett.\ 71, 2583 (1993)]. The lifetime of decaying turbulence, depending on the initial $R e_{λ, 0}$ , is predicted and found to saturate at $0.18 L^{2} / ν \propto R e_{λ, 0}^{2}$ ( $ν$ is the viscosity) for large $R e_{λ, 0}$ .

7 pages, 3 figures (available on request), file in Latex

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Universality in fully developed turbulence

Crossover from high to low Reynolds number turbulence

Abstract

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