Crossover from High to Low Reynolds Number Turbulence

The Taylor-Reynolds and Reynolds number (Re lambda and Re) dependence of the dimensionless energy dissipation rate c epsilon = epsilon L / u31,rms is derived for statistically stationary isotropic turbulence, employing the results of a variable range mean field theory. Here epsilon is the energy dissipation rate, L the (fixed) outer length scale, and u1,rms a rms velocity component. Results for c epsilon (Re lambda ) and also for Re lambda (Re) are in good agreement with experiment. Using the Re dependence of c epsilon we account for the time dependence of the mean vorticity omega (t) for decaying isotropic turbulence. The lifetime of decaying turbulence, depending on the initial Re lambda ,0 is predicted to saturate at 0.18L2 / nu [is proportional to] Re2 lambda ,0 ( nu the viscosity) for large Re lambda ,0.