Scaling Behavior of Entrainment in a TKE-l Turbulence Closure

Entrainment in a smoke cloud-topped boundary layer is investigated. It has been found that the entrainment rate in a TKE-l turbulence scheme is strongly dependent on the thickness of the radiatively cooled layer. Large Eddy Simulation (LES) models, however, predict a much weaker dependency of the entrainment rate. For the limit of very thin radiative layers the TKE-l model simulates an entrainment rate which is twice as large as in the LES models. The behavior of the LES models is predicted by a closure based on process partitioning of the buoyancy flux. In this type of closure entrainment is considered to be proportional to the part of the buoyancy flux which is directly related to the radiative cooling. On the other hand, the behavior of the TKE-l model closely follows an entrainment closure based on Eulerian partitioning of the buoyancy flux for which entrainment is determined by the integral of the buoyancy flux. It will be shown that the scaling behavior of entrainment in the E-l model can be explained by the formulation of TKE transport by downgradient diffusion. It is furthermore illustrated that the addition of a simple (pragmatic) nonlinear countergradient TKE transport term improves the bahavior of the TKE-l scheme.