UNIVERSALITY IN FULLY-DEVELOPED TURBULENCE

We extend the numerical simulations of She et al. [Phys. Rev. Lett. 70 , 3251 (1993)] of highly turbulent how with 15 less than or equal to T aylor-Reynolds numbers Re lambda less than or equal to 200 up to Re la mbda approximate to 45 000, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equatio n. First, also for these extremely high Reynolds numbers Re lambda, th e energy spectra as well as the higher moments-when scaled by the spec tral intensity at the wave number k(p) of peak dissipation-can be desc ribed by one universal function of k/k(p) for all Re lambda. Second, t he k-space inertial subrange scaling exponents zeta(m) of this univers al function are in agreement with the 1941 Kolmogorov theory (the bett er, the larger Re lambda is), as is the Re lambda dependence of k(p). Only around k(p), viscous damping leads to a slight energy pileup in t he spectra, as in the experimental data (bottleneck phenomenon).