Effect of domain size and mesh resolution on stable and unstable planetary boundary layer turbulence statistics

Wall-modeled large-eddy simulations (LES) of quasi-equilibrium stable and convective planetary boundary layers (PBLs) are carried out for different domain sizes and mesh resolutions. Wall stresses and fluxes are modeled using the Monin-Obukhov similarity theory. A Lagrangian averaged scale-dependent dynamic model is extended for a scalar field to model the sub-grid scale fluxes in the pseudo-spectral based code. The simulations are carried out on meshes varying from 32³ to 1024³. For the convective PBL, mean quantities such as velocity and temperature numerically converge with increasing grid resolution. However, higher order moments, especially the skewness of the vertical velocity, are extremely sensitive to mesh resolution. For stable PBL (GABLS1 case), doubling the domain size has no significant effect on the first order statistics, but the statistics are very sensitive to mesh resolution. With increasing mesh resolution, the height of the low-level jet (LLJ) and the boundary layer height reduces.