TY - JOUR
T1 - Asymptotic exponents from low-Reynolds-number flows
AU - Schumacher, Jörg
AU - Sreenivasan, Katepalli R.
AU - Yakhot, Victor
PY - 2007/4/11
Y1 - 2007/4/11
N2 - The high-order statistics of fluctuations in velocity gradients in the crossover range from the inertial to the Kolmogorov and sub-Kolmogorov scales are studied by direct numerical simulations (DNS) of homogeneous isotropic turbulence with vastly improved resolution. The derivative moments for orders 0 ≤ n ≤ 8 are represented well as powers of the Reynolds number, Re, in the range 380 ≤ Re ≤ 5275, where Re is based on the periodic box length L x. These low-Reynolds-number flows give no hint of scaling in the inertial range even when extended self-similarity is applied. Yet, the DNS scaling exponents of velocity gradients agree well with those deduced, using a recent theory of anomalous scaling, from the scaling exponents of the longitudinal structure functions at infinitely high Reynolds numbers. This suggests that the asymptotic state of turbulence is attained for the velocity gradients at far lower Reynolds numbers than those required for the inertial range to appear. We discuss these findings in the light of multifractal formalism. Our numerical studies also resolve the crossover of the velocity gradient statistics from Gaussian to non-Gaussian behaviour that occurs as the Reynolds number is increased.
AB - The high-order statistics of fluctuations in velocity gradients in the crossover range from the inertial to the Kolmogorov and sub-Kolmogorov scales are studied by direct numerical simulations (DNS) of homogeneous isotropic turbulence with vastly improved resolution. The derivative moments for orders 0 ≤ n ≤ 8 are represented well as powers of the Reynolds number, Re, in the range 380 ≤ Re ≤ 5275, where Re is based on the periodic box length L x. These low-Reynolds-number flows give no hint of scaling in the inertial range even when extended self-similarity is applied. Yet, the DNS scaling exponents of velocity gradients agree well with those deduced, using a recent theory of anomalous scaling, from the scaling exponents of the longitudinal structure functions at infinitely high Reynolds numbers. This suggests that the asymptotic state of turbulence is attained for the velocity gradients at far lower Reynolds numbers than those required for the inertial range to appear. We discuss these findings in the light of multifractal formalism. Our numerical studies also resolve the crossover of the velocity gradient statistics from Gaussian to non-Gaussian behaviour that occurs as the Reynolds number is increased.
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U2 - 10.1088/1367-2630/9/4/089
DO - 10.1088/1367-2630/9/4/089
M3 - Article
AN - SCOPUS:34147223030
SN - 1367-2630
VL - 9
JO - New Journal of Physics
JF - New Journal of Physics
M1 - 89
ER -