How can we describe the entrainment processes in sheared convective boundary layers?: a large-eddy simulation and mixed-layer theory/model comparison study

Dry convective boundary layers characterized by a significant wind shear on the surface and at the inversion zone are studied by means of the mixed layer theory. Two different representations of the entrainment zone, each of which has a different closure of the entrainment heat flux, are considered. The simplest of the two is based on a sharp discontinuity at the inversion (zeroth--order jump), whereas the second one prescribes a finite depth of the inversion zone (first--order jump). By using scaling arguments, we parameterize the entrainment heat flux by analyzing each term of the Turbulent Kinetic Energy equation. This parameterization is implemented in the mixed layer model. Large-eddy simulation data is used to provide the initial conditions for the mixed layer models, and to verify their results. Two different atmospheric boundary layers with different stratification in the free atmosphere are analyzed. We show that, in spite of the simplicity of the zeroth--order jump model, it provides similar results to the first--order jump model, and can reproduce the evolution of the mixed layer variables obtained by the large--eddy simulations in sheared convective boundary layers. The mixed layer model with both closures compares better with the large--eddy simulation results in the atmospheric boundary layer characterized by a moderate wind shear and a weak temperature inversio