Application of the stochastic closure theory to the Townsend-Perry constants

We compare the stochastic closure theory (SCT) to the Townsend-Perry constants as estimated from measurements in the Flow Physic Facility (FPF) at the University of New Hampshire. First, we explain the derivation of the Townsend-Perry constants, which were originally formulated by Meneveau and Marusic, in analogy with a Gaussian distribution. However, this was not supported by the data. Instead, the data show a sub-Gaussian relation that was explained by Birnir and Chen. We show herein how the SCT can be used to compute the constants, which explains their sub-Gaussian relations. We then compare the SCT theory predictions, including Reynolds-number-dependent corrections, with the data, showing good agreement.

Figure 1

The plot of $\frac{A_p}{A_2}$ against the SCT theory.

Figure 2

The plot of ${\mathit{l}}^{★}$ values that give exact agreement between the formula (18) and $\frac{A_p}{A_2}$. The inset shows the slight deviation from monotonicity at $p=6$ for small Reynolds number.

Figure 3

The plot of $A1$ against $C1$. The two are comparable for high Reynolds number. For small Reynolds number, $C1$ does not capture the mean of the fluctuation squared contained in $A1$.