Closure scheme for stably stratified turbulence without critical Richardson number

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.

Automated summary

This paper presents a new modification to the second order turbulence closure that removes the limitation posed by the critical gradient Richardson number in Mellor-Yamada style models. The newly modified model's mean wind speed and potential temperature profiles are derived in terms of similarity and structure functions, depending on the gradient Richardson number. The derivation is based on a second order boundary layer approximation under neutral to very stable stratification conditions. The paper also investigates the variances and covariances of the turbulent fluctuations with respect to the gradient Richardson number, and compares the predictions of the new model with well known existing models.