Universality in fully developed turbulence.

We extend the numerical simulations of She et al. (1993)] of highly turbulent ow with 15 Taylor-Reynolds number Re 200 up to Re 45 000, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers Re , the energy spectra as well as the higher moments { when scaled by the spectral intensity at the wave number k p of peak dissipation { can be described by one universal function of k=k p for all Re. Second, the k-space ISR scaling exponents m of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large Re is), as is the Re dependence of k p. Only around k p viscous damping leads to slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).