Nonlinear Sciences – Chaotic Dynamics
Scientific paper
1993-12-03
Phys. Rev. E50, 2784-2789 (1994)
Nonlinear Sciences
Chaotic Dynamics
14 pages, Latex, 5 figures (on request), 3 tables, submitted to Phys. Rev. E
Scientific paper
10.1103/PhysRevE.50.2784
We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70, 3251 (1993)] of highly turbulent flow with $15 \le$ Taylor-Reynolds number $Re_\lambda\le 200$ up to $Re_\lambda \approx 45000$, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers $Re_\lambda$, 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 {\it one universal} function of $k/k_p$ for all $Re_\lambda$. Second, the ISR scaling exponents $\zeta_m$ of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large $Re_\lambda$ is), as is the $Re_\lambda$ 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).
Grossmann Siegfried
Lohse Detlef
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