3 D ec 1 99 3 Universality in fully developed turbulence

We extend the numerical simulations of She et al. [Phys. Rev. Lett. 70, 3251 (1993)] of highly turbulent flow with 15 ≤ Taylor-Reynolds number Reλ ≤ 200 up to Reλ ≈ 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 Reλ, the energy spectra as well as the higher moments – when scaled by the spectral intensity at the wave number kp of peak dissipation – can be described by one universal function of k/kp for all Reλ. Second, the ISR scaling exponents ζm of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large Reλ is), as is the Reλ dependence of kp. Only around kp viscous damping leads to slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).