The effect of mesh resolution on convective boundary layer statistics and structures generated by large-eddy simulation

A massively parallel large-eddy simulation (LES) code for planetary boundary layers (PBLs) that utilizes pseudospectral differencing in horizontal planes and solves an elliptic pressure equation is described. As an application, this code is used to examine the numerical convergence of the three-dimensional time-dependent simulations of a weakly sheared daytime convective PBL on meshes varying from 32³ to 1024³ grid points. Based on the variation of the second-order statistics, energy spectra, and entrainment statistics, LES solutions converge provided there is adequate separation between the energy-containing eddies and those near the filter cutoff scale. For the convective PBL studied, the majority of the low-order moment statistics (means, variances, and fluxes) become grid independent when the ratio z_i/(C_sΔ_f)>310, where z_i is the boundary layer height, Δ_f is the filter cutoff scale, and C_s is the Smagorinsky constant. In this regime, the spectra show clear Kolmogorov inertial subrange scaling. The bulk entrainment rate determined from the time variation of the boundary layer height w_e = dz_i/dt is a sensitive measure of the LES solution convergence; w_e becomes grid independent when the vertical grid resolution is able to capture both the mean structure of the overlying inversion and the turbulence. For all mesh resolutions used, the vertical temperature flux profile varies linearly over the interior of the boundary layer and the minimum temperature flux is approximately -0.2 of the surface heat flux. Thus, these metrics are inadequate measures of solution convergence. The variation of the vertical velocity skewness and third-order moments expose the LES's sensitivity to grid resolution.