Title: Reynolds number dependence of the structure functions in homogeneous turbulence,
Abstract: We compare the predictions of stochastic closure theory (SCT) with
experimental measurements of homogeneous turbulence made in the Variable
Density Turbulence Tunnel (VDTT) at the Max Planck Institute for Dynamics and
Self-Organization in Gottingen. While the general form of SCT contains
infinitely many free parameters, the data permit us to reduce the number to
seven, only three of which are active over the entire inertial range. Of these
three, one parameter characterizes the variance of the mean field noise in SCT
and another characterizes the rate in the large deviations of the mean. The
third parameter is the decay exponent of the Fourier variables in the Fourier
expansion of the noise, which characterizes the smoothness of the turbulent
velocity. SCT compares favorably with velocity structure functions measured in
the experiment. We considered even-order structure functions ranging in order
from two to eight as well as the third-order structure functions at five
Taylor-Reynolds numbers (Rl) between 110 and 1450. The comparisons highlight
several advantages of the SCT, which include explicit predictions for the
structure functions at any scale and for any Reynolds number. We observed that
finite-Rl corrections, for instance, are important even at the highest Reynolds
numbers produced in the experiments. SCT gives us the correct basis function to
express all the moments of the velocity differences in turbulence in Fourier
space. The SCT produces the coefficients of the series and so determines the
statistical quantities that characterize the small scales in turbulence. It
also characterizes the random force acting on the fluid in the stochastic
Navier-Stokes equation, as described in the paper.