Closure scheme for stably stratified turbulence without critical Richardson number

Abstract

This paper presents a new modification of the second order turbulence closure that removes the critical gradient Richardson number limitation typically found in Mellor-Yamada style models. The mean wind speed and potential temperature profiles are derived for the newly modified model in terms of similarity and structure functions depending on the gradient Richardson number. The derivation is based on a second order boundary layer approximation in neutral to very stable stratification conditions. Some recent closure assumptions for pressure-temperature and heat flux are considered. Variances and covariances of the turbulent fluctuations are also investigated with respect to the gradient Richardson number. The new model predictions are confronted with some well known models.