Galperin, B., L. H. Kantha, S. Hassid, and A. Rosati, 1988: A quasi-equilibrium turbulent energy model for geophysical flows. Journal of the Atmospheric Sciences, 45(1), 55-62.

Abstract: The Mellor-Yamada hierarchy of turbulent closure models is reexamined to show that the elimination of a slight inconsistency in their analysis leads to a quasi-equilibrium model that is somewhat simpler than their level 2 1/2 model. Also the need to impose realizability conditions restricting the dependence of exchange coefficients on shearing rates is eliminated. The model is therefore more robust while the principal advantage of the level 2 1/2 model, namely the solution of a prognostic equation for turbulent kinetic energy is retained. Its performance is shown to be not much different than that of level 2 1/2.