Abstract
Monin–Obukhov similarity theory is used in large-eddy simulation (LES) models as a surface boundary condition to predict the surface shear stress and scalar fluxes based on the gradients between the surface and the first grid level above the surface. We outline deficiencies of this methodology, such as the systematical underestimation of the surface shear stress, and propose a modified boundary condition to correct for this issue. The proposed boundary condition is applied to a set of LES for both neutral and stable boundary layers with successively decreasing grid spacing. The results indicate that the proposed boundary condition reliably corrects the surface shear stress and the sensible heat flux, and improves grid convergence of these quantities. The LES data indicate improved grid convergence for the surface shear stress, more so than for the surface heat flux. This is either due to a limited performance of the Monin–Obukhov similarity functions or due to problems in the LES model in representing stable conditions. Furthermore, we find that the correction achieved using the proposed boundary condition does not lead to improved grid convergence of the wind-speed and temperature profiles. From this we conclude that the sensitivity of the wind-speed and temperature profiles in the LES model to the grid spacing is more likely related to under-resolved near-surface gradients and turbulent mixing at the boundary-layer top, to the SGS model formulation, and/or to numerical issues, and not to deficiencies due to the use of improper surface boundary conditions.
Highlights
One persisting problem in large-eddy simulation (LES) of the atmospheric boundary layer is the so-called logarithmic layer mismatch, the fact that the simulated wind-speed profile does not match the predicted logarithmic relation, a direct result of the inherent inability of LES models to resolve locally the dominant eddies close to the surface
In line with previous research, we found a non-convergence of the surface shear stress and heat flux for both neutral and stable boundary layers, suggesting that the non-convergence in LES models in the stable boundary layer might be related to the outlined issues of the surface boundary condition
In order to evaluate the two different applied boundary conditions, we first compare the results of IL and elevated SG” (ESG) methods for purely neutral conditions and neglect the possible complications imposed by stratification
Summary
One persisting problem in large-eddy simulation (LES) of the atmospheric boundary layer is the so-called logarithmic layer mismatch, the fact that the simulated wind-speed profile does not match the predicted logarithmic relation, a direct result of the inherent inability of LES models to resolve locally the dominant (small) eddies close to the surface. In this region, the subgrid-scale (SGS) turbulence parametrization dominates the flow. The vertical extent of the surface layer is commonly defined to be that region in which the turbulent fluxes do not vary more than ≈ 10% of their surface values. Due to the linear decrease with height (observed in steady-state conditions) the depth of the surface layer can be loosely estimated to be ≈ 10% of the boundary-layer depth
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