Finite-difference large-eddy simulations of atmospheric turbulence using a Lagrangian scale-dependent sub-grid scale model

Large-eddy simulations (LES) have been successfully utilized in many atmospheric turbulence studies. In LES, grid spacing acts like a low-pass filter such that flow features larger than the grid spacing can be resolved, whereas the effects of smaller, sub-grid scale (SGS) eddies are modeled. Therefore, a well-designed SGS model plays a vital role in a successful LES. One of the most sophisticated SGS models is the Lagrangian scale-dependent (LASD) model, in which the scale-dependence of the Smagorinsky coefficient C_S is taken into account by performing two explicit filtering processes with different filter widths. Then Lagrangian averaging in time along flow trajectories is used to eliminate the numerical instability caused by backscattering. The LASD model has been successfully implemented in atmospheric boundary layer (ABL) studies using the spectral/pseudo-spectral methods. However, it has not been coupled with finite-difference methods.

In this study, the finite-difference method is used for the first time in LES of the ABL using an LASD subgrid scale model. First, a-posteriori tests with a fully conservative 4^th-order scheme are performed by simulating turbulent channel flows with . Vertical profiles of mean wind velocity, turbulence intensity, and momentum fluxes, and 1-D spectra of streamwise velocity are compared to those from an existing direct numerical simulation (DNS) database. Several different SGS models are compared and a sensitivity test of spatial resolution is also performed. Second, LES of a neutral ABL with (i.e., molecular viscosity is negligible) are performed using the same numerical methods. The classic logarithmic profile of the streamwise velocity in the inertial subrange is examined in particular. Third, the numerical methods are extended to LES of a stable ABL where the buoyancy effect is considered by using the Boussinesq approximation. The SGS heat flux is calculated via an LASD model similar to that for the SGS stress. The results are compared to the GEWCE Atmospheric Boundary Layer Study (GABLS) database.