Large-Eddy Simulation of Convective Boundary Layer with Density Stratification

Abstract

Large-eddy simulation of convective boundary layer is performed without and with density stratification using a fully compressible nonhydrostatic model. Effect of density stratification in the boundary layer, where Bousinessq model has normally been applied for the analysis, is investigated by comparing the two cases. This investigation also reveals the difference between Bussinesq model and the fully compressible model, which is hardly used in boundary layer analysis. Although the potential temperature with identical neutral distribution is used for the both cases, the boundary layer height of the stratified case is limited to less than half height of the non-stratified case. The cause is considered to be derived from suppression force to the buoyancy. The suppression force is analyzed in terms of the forces working vertically. It is found that vertical pressure gradient shows symmetrical distribution to that of buoyancy force, and the fact indicates that hydrostatic relation between density and pressure is quickly recovered due to the Brunt-Väisälä oscillation. The effect is also explained by the positive Brunt-Väisälä frequency derived from vertical density gradient in the stratified case. As the results, convective boundary layer with density stratification becomes more stable than that expected from the neutral potential temperature profile. The results of the present study indicate that small density stratification cannot be neglected even for simulating convective boundary layer, and Boussinesq approximation which neglects density gradient may cause significant errors. The present results also suggest a problem that a planetary boundary layer scheme based on Boussinesq model will be inconsistent with a mesoscale model which mainly employs fully compressible nonhydrostatic equations.