Energy-similarity -- a new turbulence closure model for the stably stratified atmospheric boundary layer

A new turbulence closure model for stably stratified shear-driven turbulence based on observational evidence, presented by Mauritsen and Svensson (see additional submitted abstract), is developed. It uses the concept of turbulent energy, which is the sum of the turbulent kinetic and turbulent potential energies. The latter is related to the temperature variance. The prognostic budget equation for turbulent energy contains only a shear production term, viscous dissipation and storage.

The closure uses empirical functions of the gradient Richardson number for the non-dimensional fluxes of momentum and heat, estimated by Mauritsen and Svensson, in addition to an empirical dissipation length scale.

The length-scale contains three physical constants: von Karmans constant, one for neutrally stratified conditions and one for stably stratified conditions. The latter two are determined by the use of a hundred high-resolution large eddy simulations (LES), covering four classes of neutral and stratified boundary layers ranging from 10 to 3000 meters depth. It is found that the closure is able to reproduce the results of that particular LES-model to within 20 percent, by the tuning the two free constants.

The closure is then independently tested against the first GABLS LES case, which is situated in the middle of the stability range used for the calibration.