  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.
