Design of a Nonsingular Level 2.5 Second-Order Closure Model for the Prediction of Atmospheric Turbulence

Abstract The behavior of the Mellor and Yamada Level 2.5 second-order turbulence closure model is analyzed over its entire domain of definition on the Ri × q2/qe2 plane, where Ri is the Richardson number of the mean flow and where q2/qe2 is the ratio of the turbulent kinetic energy predicted by the model to that which would obtain in a state of local equilibrium. The Level 2.5 model is reasonably accurate over the subdomain q2/qe2 ∼ 1, but it becomes unrealistic and pathological for the case of decaying turbulence (q2/qe2 < 1). The model is modified for the case of growing turbulence to rectify some of its physical shortcomings for that case, and to remove the pathologies that prohibit its use in a general circulation model. The modified model attempts to take into account the effects of the growth rate, advection and vertical turbulent diffusion terms in the balance equations for all of the second moments, as well as the effects of the rapid return-to-isotropy or scrambling terms in the equations for the...