Dynamical equations for high-order structure functions, and a comparison of a mean field theory with experiments in three-dimensional turbulence

Abstract

Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) and R.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two different approaches that have the Navier-Stokes equations as the common starting point, a set of steady-state dynamic equations for structure functions of arbitrary order in hydrodynamic turbulence. These equations are not closed. Yakhot proposed a "mean field theory" to close the equations for locally isotropic turbulence, and obtained scaling exponents of structure functions and an expression for the tails of the probability density function of transverse velocity increments. At high Reynolds numbers, we present some relevant experimental data on pressure and dissipation terms that are needed to provide closure, as well as on aspects predicted by the theory. Comparison between the theory and the data shows varying levels of agreement, and reveals gaps inherent to the implementation of the theory.

16 pages, 23 figures

References in corpus (2)

• The multifractal nature of turbulent energy dissipation
• Equations relating structure functions of all orders

Cited by in corpus (9)

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• Local 4/5-Law and Energy Dissipation Anomaly in Turbulence
• Scaling exponents saturate in three-dimensional isotropic turbulence
• Probability Densities in Strong Turbulence
• Yakhot's model of strong turbulence: A generalization of scaling models of turbulence
• Closure of two dimensional turbulence: the role of pressure gradients
• Self-organization and Nonuniversal Anomalous Scaling in Non-Newtonian Turbulence
• Transverse velocities, intermittency and asymmetry in fully developed turbulence