Explicit Filtering in Large Eddy Simulation of Barotropic Turbulence in Spectral Space

Explicit filtering in large eddy simulation (LES) of a turbulent barotropic flow on the sphere in spectral space is studied and compared to implicit filtering. Here, a smooth filter is applied to the nondivergent barotropic vorticity equation (BVE) on the rotating sphere to divide the flow field into resolved scale (RS) and subfilter scale (SFS) motions. A portion of the SFS motions are reconstructed theoretically using the approximate deconvolution model (ADM). While the unreconstructed portion consists of the subgrid scale (SGS) motions and needs to be modeled separately. In order to investigate the effects of the explicit filtering alone no SGS model is used. It is shown that the explicit filtering accurately tracks the evolution of the coherent structures in two-dimensional turbulent flow on the rotating sphere, whereas the implicit filtering does not. It is also shown that explicit filtering improves the results of the temporal variation of the total kinetic energy and the total enstrophy and the variation of the energy spectrum with wavenumber compare to the implicit filtering. Although explicit filtering is more expensive than implicit filtering it increases the accuracy of the computations and improves the results, particularly where the location of coherent structures is concerned, a topic of particular importance in LES of atmospheric flows for climate and weather applications.