Three regularization models as large-eddy simulations

We test three regularizations, the $\alpha-$model, {Leray$-\alpha$}, and {Clark$-\alpha$}, as sub-grid models for LES by comparison with a $1024^3$ direction numerical simulation (DNS), $R_\lambda \approx 800$, with a Taylor-Green forcing. Both the $\alpha-$model and {{Clark$-\alpha$} }are able to reproduce the large-scale anisotropy of the flow as well as the time scale of developing turbulence. {{Leray$-\alpha$} }fails in both these regards. We study intermittency corrections through pdfs and the anomalous scaling of the velocity increment structure functions. {{Leray$-\alpha$} }is somewhat less intermittent than the DNS and produces an energy spectrum that is too shallow in the inertial range, while {{Clark$-\alpha$} }produces a broad $k^{-5/3}$ spectrum and stronger intermittency corrections. Finally, the agreement of the DNS and $\alpha-$model spectra, in disparity with results for lower Reynolds number simulations, is worse than in the Clark$-\alpha$ model. We conjecture that this enhanced intermittency in the $\alpha$ model is related to the steeper than $k^{-5/3}$ spectrum now reported for the very highest Reynolds number simulations and atmospheric observations.