Mixing Length in the Surface Layer matching the Similarity Theory in a single column TKE framework

For many modelling applications, it is commonly assumed that the size of the turbulent eddies in the ABL is reduced near the ground such as its characteristic dimension can be made proportional to the height at which the eddies are parametrized within the model.

The classical choice for turbulence schemes using a mixing length for its closure has been to take the mixing length in the surface layer as L=kappa z, where kappa=0.4 stands for the von Karman constant. Using a 1.5 order turbulence scheme within the Meso-NH model, this formulation of $L$ in the surface layer did not yield better results than to just ignore it. This result is true both in LES mode (3D subgrid turbulence scheme) and in mesoscale mode (1D turbulence scheme).

Redelsperger and Mahe (2000) have proposed a new formulation for the mixing length in the surface layer, consistent with both the Similarity theory and the Turbulence Kinetic Energy equation. For neutral conditions L=2.79 z is found, while for stratified conditions the proportionality coefficient is a function of stability parameters.

The 1D tests of the latter formulation in free convective, convective with wind and neutrally stratified shear driven boundary layers show better behaviour of the surface layer wind gradients and a more comprehensive TKE budget compared to the LES outputs and the similarity functions.