Scaling analysis of the turbulent kinetic energy at the entrainment zone in sheared convective boundary layers

Boundary layer growth depends strongly on the entrainment of heat at the top of the convective boundary layer. This process is driven by convective turbulence transported from the mixed layer and the local shear at the inversion. In order to be able to represent this process in large scale atmospheric models, it is fundamental to understand the main processes which produce and dissipate turbulent kinetic energy in the entrainment zone.

By performing systematic numerical Large-Eddy Simulation (LES) experiments, we analyze the contributions of the different turbulent kinetic energy (TKE) budget terms in the entrainment zone. The influence of shear on the boundary layer growth evolution was studied by increasing the initial wind speed. The main result of this sensitivity analysis is that convective boundary layer deepens with increasing wind speed due to the enhancement of the heat entrainment flux by the presence of shear.

Regarding the evolution of the different terms of the TKE budget at the inversion, the following results are found. First, as was expected, shear contribution increases with increasing geostrophic wind and the relation is clearly nonlinear. For winds above 10 m s-1 the shear term is the largest budget contribution in the entrainment zone. Second, the sum of transport and pressure terms decreases its value at the inversion level when shear increases. For all the prescribed sheared convective boundary layers, surface shear is no longer transported to the entrainment zone. That is, all the shear available for the entrainment is locally produced at the entrainment zone. The sum of these two terms can even become a destruction TKE term at the entrainment zone. Third, the time tendency term of TKE remains small in all the analyzed cases. Finally, the TKE dissipation increases with shear and presents a similar profile with height to shear. However, in the entrainment zone the dissipation alone is not able to compensate shear production; in large shear cases this shear excess is the main source of TKE at the entrainment zone.

Convective and local scaling arguments are applied to scale the TKE budget terms. The TKE contribution characterized by mixed layer properties are scaled by using the boundary layer depth and the convective velocity. Physical processes localize at the entrainment zone are made non dimensional by the inversion layer thickness, the module of the horizontal velocity jump and the momentum fluxes. In all the studied numerical experiments, friction velocity does not play a significant role in the physical processes at the inversion zone. A good fit of the TKE budget terms is obtained with the scaling, especially for shear contribution.