Large-eddy simulations often use a subgrid model which is characterized by a length scale. Cs is commonly defined to be equal to the ratio of this length scale to the scale of the computational mesh. Mason and Callen argued that the subgrid model and its length scale define and impose the filter operation of the large-eddy simulation. They saw Cs as a measure of numerical accuracy. Others have sought to link the filter operation to the computational mesh and have therefore viewed Cs as needing determination for correct implementation.
In the present study, a large number of simulations have been performed of the convective atmospheric boundary layer in order to discrimiante between these views. These have used a number of different values of subgrid length scale, and a variety of different resolutions (with the highest resolution simulations having over 200 grid points in each
direction).
The results of six simulations with the same value of subgrid length
scale but with different resolutions (and hence different values of
Cs) are compared. The spectra (and all other statistics) from the four simulations with Cs between 0.23 and 0.8 are very similar, consistent with the idea that they are four solutions to the same continuous problem i.e. the filter is set by the subgrid model, which is the same in all cases, and not by the numerical grid, which is varying. The use of smaller values of Cs is shown to lead to less satisfactory behaviour, with a build up of spectral energy close to the grid scale and evidence for contamination by finite difference errors. Comparison is also made between simulations with fixed resolution and varying length scale, and with varying resolution and length scale at fixed Cs.
For the case of buoyant convection, the buoyancy dependence of the
subgrid model is further examined. It is common to allow the subgrid
length scale to decrease in conditions of stable stratificiation, but to keep it constant in unstable conditions. It is shown that this may lead to a build up of spectral energy at and close to the grid scale as the surface is approached. In contrast, allowing the length scale to increase in unstable conditions is shown to be more consistent with a fixed filter operation