Direct Numerical Simulation of the Convective Boundary Layer

The inversion of the dry shear-free Convective Boundary Layer is investigated by means of Direct Numerical Simulation (DNS). This work is motivated by the importance of entrainment and related mechanisms at the inversion of the atmospheric boundary layer, combined with the uncertainty of Large-Eddy Simulations (LES) there. Despite moderate Reynolds numbers attainable, results show that the achieved scale separation is enough to capture the expected $1/2$ power law evolution in time, and the expected structure---an inversion-capped outer layer, whose statistics are comparable to LES results and atmospheric data when normalized with the convective scales, and an inner layer near the surface comparable to that of the heated plate case. In agreement with some previous investigations, the entrainment ratio $A$ is a factor of two less than the nominal $0.2$ even though the corresponding entrainment velocity is within 5\% of the Zero-order Model prediction with $A=0.2$. To understand this apparent discrepancy, we use DNS data to directly determine the behavior of the terms of an exact equation for the entrainment ratio.