Toward Numerical Modeling in the “Terra Incognita”

TLDR

In mesoscale modeling the turbulence scale l is much smaller than the filter scale Δ, whereas in LES it is much larger, creating a numerical region called the terra incognita where l and Δ are comparable. They extend the standard scalar eddy‑diffusivity subfilter‑scale model by incorporating the neglected production terms, yielding a tensorial eddy‑diffusivity formulation. HATS data reveal that the neglected production terms are significant, and the resulting tensorial SFS model could enhance performance in the terra incognita, though it is likely unnecessary for fine‑ or coarse‑resolution LES or mesoscale simulations.

Abstract

In mesoscale modeling the scale l of the energy- and flux-containing turbulence is much smaller than the scale Δ of the spatial filter used on the equations of motion, and in large-eddy simulation (LES) it is much larger. Since their models of the subfilter-scale (SFS) turbulence were not designed to be used when l and Δ are of the same order, this numerical region can be called the “terra incognita.” The most common SFS model, a scalar eddy diffusivity acting on the filtered fields, emerges from the conservation equations for SFS fluxes when several terms, including all but one of the production terms, are neglected. Analysis of data from the recent Horizontal Array Turbulence Study (HATS) shows that the neglected production terms can be significant. Including them in the modeled SFS flux equations yields a more general SFS model, one with a tensor rather than a scalar eddy diffusivity. This more general SFS model is probably not necessary in fine-resolution LES or in coarse-resolution mesoscale modeling, but it could improve model performance in the terra incognita.