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On the Stochastic Closure Theory of Homogeneous Turbulence


We compare the predictions of the stochastic closure theory (SCT) [1] with experimental

data obtained in the Variable Density Turbulence Tunnel (VDTT) [2], at the Max Planck Institute

for Dynamics and Self-Organization in G¨ottingen. The mean flow in the homogeneous

turbulence experiment reduces the number of parameters in SCT to just three, one characterizing

the variance of the mean field noise and another characterizing 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. This characterizes the smoothness of the turbulent velocity.

We compare the data for the even-order longitudinal structure functions ranging from the

the second to the eighth structure function as well as the third-order structure function, to

the SCT theory with generic noise, depending on the above three parameters, at five Taylor-

Reynolds (Rl) numbers ranging from 110 to 1450. The theory gives excellent comparisons

with data for all the structure functions and for all the Taylor-Reynolds numbers. This highlights

the advantage of the SCT theory, where the structure functions can be computed explicitly

and their dependence on the Rl number computed. These results are robust with respect

to the size of dissipation range filters applied to the data, and comparisons to the fits without

the Rl number corrections show a clear improvement when the corrections are present. This

improvement is significant for the lower Rl number and disappears as the Rl number becomes

large, as expected. Very surprisingly the comparison of SCT and the data also gives information about the

smoothness of the turbulent velocity as Rl becomes very large.

We then compare the SCT to the Townsend-Perry constants generated in the flow physics

facility (FPF) at the University of New Hampshire. The Reynolds correction terms in the SCT

changed the initial derivation of this similarity, forcing a refinement of the theory. Once done,

we see good agreement between the data and the SCT.

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