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Two recent publications [V. Yakhot, Phys. Rev. E {\bf 63}, 026307, (2001) andR.J. Hill, J. Fluid Mech. {\bf 434}, 379, (2001)] derive, through two differentapproaches that have the Navier-Stokes equations as the common starting point,a set of steady-state dynamic equations for structure functions of arbitraryorder in hydrodynamic turbulence. These equations are not closed. Yakhotproposed a "mean field theory" to close the equations for locally isotropicturbulence, and obtained scaling exponents of structure functions and anexpression for the tails of the probability density function of transversevelocity increments. At high Reynolds numbers, we present some relevantexperimental data on pressure and dissipation terms that are needed to provideclosure, as well as on aspects predicted by the theory. Comparison between thetheory and the data shows varying levels of agreement, and reveals gapsinherent to the implementation of the theory.Comment: 16 pages, 23 figure

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