On the entrainment law at the top of the convectively-driven atmospheric boundary layer

We discuss the entrainment processes at the top of the convectively-driven boundary layer. The discussion is based on results from a high-resolution (256 3 grid points) large-eddy simulation initialized by a commonly used sounding of Day 33 of the Wangara experiment. We find that the mixed-layer turbulence precisely follows the Kolmogorov spectral law for the velocity field, whether two-dimensional (in horizontal planes) or one-dimensional spectra are computed. This behavior also holds for the frequency spectrum, when the Taylor's frozen turbulence hypothesis is used. As well, the fluctuating virtual potential temperature field follows the Corrsin-Oboukhov spectral law. The multiplicative constants of the power laws, inferred from the compensated spectra, are found to be in good agreement with previous measurements in the atmosphere. We next revisit the entrainment law at the mixed-layer top from two complementary Eulerian and Lagrangian approaches. The Lagrangian approach yields similar results to the eulerian one: the normalized entraine-ment velocity $w_e/w_⋆$, where we and $w_⋆$ are the entrainment and convective velocities, is found to vary as a function of the bulk Froude number squared at the interface with a multiplicative constant close to 1.2