Employing Taylor and Heisenberg subfilter viscosities to simulate turbulent statistics in LES models

A turbulent subfilter viscosity for Large Eddy Simulation (LES) based on the Taylor statistical
diffusion theory is proposed. This viscosity is described in terms of a velocity variance
and a time scale, both associated to the inertial subrange. This new subfilter viscosity
contains a cutoff wavenumber kc , presenting an identical form (differing by a constant)
to the Heisenberg subfilter viscosity. Therefore, both subfilter viscosities are described
in terms of a sharp division between large and small wavenumbers of a turbulent flow
and, henceforth, Taylor and Heisenberg subfilter viscosities are in agreement with the
sharp Fourier filtering operation, frequently employed in LES models. Turbulent statistics
of different orders, generated from atmospheric boundary layer simulations employing
both Taylor and Heisenberg subfilter viscosities have been compared with observations and
results provided by other simulations. The comparison shows that the LES model utilizing
the approaches of Taylor and Heisenberg reproduces these turbulent statistics correctly in
different vertical regions of a planetary convective boundary layer (CBL).