Dynamical equations for high-order structure functions, and a comparison of a mean-field theory with experiments in three-dimensional turbulence - art. no. 056302

Two recent papers [V. Yakhot, Phys. Rev. E 63. 026307, (2001) and R. J. Hil l, J. Fluid Mech. 434, 379, (2001)] derive, through two different approache s that have the Navier-Stokes equations as the common starting point. a set of dynamic equations for structure functions of arbitrary order in turbule nce. These equations are not closed. Yakhot proposed a "mean-field theory" to close the equations for locally isotropic turbulence, and obtained scali ng exponents of structure functions and expressions for the peak in the pro bability density function of transverse velocity increments, and for its be havior for intermediate amplitudes. At high Reynolds numbers, some relevant experimental data on pressure gradient and dissipation terms are presented that are needed to provide closure, as well as on other aspects predicted by the theory. Comparison between the theory and the data shows varying lev els of agreement, and reveals gaps inherent to the implementation of the th eory.