# Asymptotic exponents from low-Reynolds-number flows

@article{Schumacher2006AsymptoticEF,
title={Asymptotic exponents from low-Reynolds-number flows},
author={J{\"o}rg Schumacher and Katepalli R. Sreenivasan and Victor Yakhot},
journal={New Journal of Physics},
year={2006},
volume={9},
pages={89 - 89}
}
• Published 27 April 2006
• Physics
• New Journal of Physics
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 Lx. These low-Reynolds-number flows give no hint of…
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## References

SHOWING 1-10 OF 29 REFERENCES
Anomalous scaling of low-order structure functions of turbulent velocity
• Physics
Journal of Fluid Mechanics
• 2005
It is now believed that the scaling exponents of moments of velocity increments are anomalous, or that the departures from Kolmogorov's (1941) self-similar scaling increase nonlinearly with the
High-order velocity structure functions in turbulent shear flows
• Physics
Journal of Fluid Mechanics
• 1984
Measurements are presented of the velocity structure function on the axis of a turbulent jet at Reynolds numbers Rλ ≤ 852 and in a turbulent duct flow at Rλ = 515. Moments of the structure function
Mean-field approximation and a small parameter in turbulence theory.
• V. Yakhot
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2001
It is shown that in the vicinity of d=d(c) the ratio of the relaxation and translation characteristic times decreases to zero, thus giving rise to a small parameter of the theory, and predicted that the single-point probability density function of transverse velocity components in developing as well as in the large-scale stabilized two-dimensional turbulence is a Gaussian.
Does deterministic chaos imply intermittency in fully developed turbulence
• Physics
• 1991
A Fourier–Weierstrass decomposition of the velocity field is introduced. The admitted number of real amplitudes is 572 or 836. They are determined numerically from the Navier–Stokes equation
Relation between shear parameter and Reynolds number in statistically stationary turbulent shear flows
Studies of the relation between the shear parameter S* and the Reynolds number Re are presented for a nearly homogeneous and statistically stationary turbulent shear flow. The parametric
On the rapid increase of intermittency in the near-dissipation range of fully developed turbulence
• Physics
• 2005
Abstract. Intermittency, measured as $\log \left({F(r)}/{3}\right)$, where F(r) is the flatness of velocity increments at scale r, is found to rapidly increase as viscous effects intensify, and
Dynamical equations for high-order structure functions, and a comparison of a mean-field theory with experiments in three-dimensional turbulence.
• Physics
Physical review. E, Statistical, nonlinear, and soft matter physics
• 2001
Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory, as well as on other aspects predicted by the theory.
Role of Pressure in Turbulence
• Physics
• 2003
There is very limited knowledge of the kinematical relations for the velocity structure functions higher than three. Instead, the dynamical equations for the structure functions of the velocity
Some specific features of atmospheric turbulence
The specific features of atmospheric turbulence can hardly be observed in the laboratory and should be studied in the atmosphere, where the range of scales of disturbances is very broad. Slow