Crossover from high to low Reynolds number turbulence.

The Taylor-Reynolds and Reynolds number (Reλ and Re) dependence of the dimensionless energy dissipation rate cǫ = ǫL/u 3 1,rms is derived for statistically stationary isotropic turbulence, employing the results of a variable range mean field theory. Here, ǫ is the energy dissipation rate, L is the (fixed) outer length scale, and u1,rms a rms velocity component. Our fit-parameter free results for cǫ(Reλ) and also for Reλ(Re) are in good agreement with experimental data. Using the Re-dependence of cǫ 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 Reλ,0, is predicted and found to saturate at 0.18L/ν ∝ Reλ,0 (ν is the viscosity) for large Reλ,0. PACS: 47.27.-i, 47.27.Gs