Universality in fully developed turbulence

Abstract

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 $R{e}_{\lambda }\le 200$ up to $R{e}_{\lambda }\approx 45000$, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers $R{e}_{\lambda }$, 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 $R{e}_{\lambda }$. Second, the ISR scaling exponents ${\zeta }_m$ of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large $R{e}_{\lambda }$ is), as is the $R{e}_{\lambda }$ 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).

14 pages, Latex, 5 figures (on request), 3 tables, submitted to Phys. Rev. E

References in corpus (3)

• The multifractal nature of turbulent energy dissipation
• Scale resolved intermittency in turbulence
• Finite size corrections to scaling in high Reynolds number turbulence

Cited by in corpus (18)

• Bottleneck effects in turbulence: Scaling phenomena in r- versus p-space
• Scaling and Dissipation in the GOY Shell Model
• Exact solutions of closed string theory
• Crossover from high to low Reynolds number turbulence
• Transition to Chaos in a Shell Model of Turbulence
• Helical shell models for three dimensional turbulence
• Different intermittency for longitudinal and transversal turbulent fluctuations
• Finite size corrections to scaling in high Reynolds number turbulence
• Response maxima in time-modulated turbulence: Direct Numerical Simulations
• How the viscous subrange determines inertial range properties in turbulence shell models
• Response maxima in modulated turbulence Part II: Numerical simulations
• Links between dissipation, intermittency, and helicity in the GOY model revisited
• Transitions and Probes in Turbulent Helium
• Fractal dimension crossovers in turbulent passive scalar signals
• Graded Contractions of Affine Kac-Moody Algebras
• Qian Jian and His Contribution to Small-Scale Turbulence Studies
• Dynamical model of steadily forced isotropic turbulence
• Does intermittency affect the inertial transfer rate in stationary isotropic turbulence?