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The following HTML text is provided to enhance online readability. Many aspects of typography translate only awkwardly to HTML. Please use the page image as the authoritative form to ensure accuracy. the rms velocity was equal to one. This process was repeated until the shape of spectrum did not change. The Taylor Reynolds number at this point was Rλ=46. Figure 3 compares energy spectrums of numerical simulations to the measurements of Comte-Bellot and Corrsin [2]. The energy density and the wavenumbers are normalized using Kolmogorov units. The numerical simulations include the results of 1283 psuedo-spectral simulations (labeled I and II), and eight-point and six-point upwindbiased finite-difference codes2. The first spectral simulation was allowed to naturally decay. The second spectral simulation forced the lowest wavenumbers to make the spectrum stationary. The six-point FDM scheme is used in our free-surface code. The results of the eight-point FDM scheme are included to illustrate convergence. The finite-difference codes compare as well to the experiments as the spectral codes. Moreover, the finite-difference codes show no evidence of an energy pileup at the highest wavenumbers, unlike the spectral codes. Except for the energy pileup, a nonstationary spectrum may explain the poorer agreement of the first spectral simulation with the experimental data. The poorer agreement of the second spectral simulation at the lower wavenumbers may be attributed to the forcing. As expected, the eight-point finite-difference scheme shows slightly better agreement with the experimental data at the highest wavenumbers. However, considering that this slight discrepancy is occuring at the Nyquist wavenumbers, the excellent agreement of both finite-difference codes with the experimental data is remarkable. We are currently investigating the performance of the finite-difference codes at higher Reynolds numbers on a CM-5 computer. The DNS dataset from the eight-point finite-difference code is used to generate synthetic LES velocity fields using different filters. The SGS stress tensor is calculated using the definition in Equation (6). Then volume-averaged SGS coefficients are calculated using Lilly 's least-squares procedure. Table 6 provides the SGS coefficients and the correlation coefficients. The effective lengthscale of each filter is Δe, and Δ is the grid spacing. As the ratio Δe/Δ gets larger, more energy is filtered out. Two of the filters correspond to the grid and test filters that are defined in Equations (22 & 23). The third filter is a very coarse second-order accurate filter. The correlation coefficient is defined below:
where Table 6: SGS and correlation coefficients.
In Table 6 the correlation of the global model (Types II and V) is much better than the local models (Types I and IV), and the combination of a local model with the global model (Type III) does not improve the performance of the global model alone (Type II). In general, the correlations of the global models slightly decrease as the coarseness of the filter increases, whereas the correlations
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, (33)
is the SGS stress tensor and 
is the model SGS stress tensor. The brackets denote volume averaging.