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/q_e² plane, where Ri is the Richardson number of the mean flow and where q²/q_e² 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/q_e² ∼ 1, but it becomes unrealistic and pathological for the case of decaying turbulence (q²/q_e² < 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 anisotropic components of the moments. The performance of the modified Level 2.5 model has been tested and compared to the performance of various other modified versions of the model through the numerical simulation of a growing convective planetary boundary layer. The modified Level 2.5 model gives a realistic-looking simulation of the evolution of the second turbulent moments at the 300 m level. The scheme approaches the same asymptotic state as does the turbulent kinetic energy adjustment scheme, but the modified Level 2.5 model predicts a longer period of transience. The TKE-adjustment scheme reduces to the Level 2 model during the growth phase of turbulence. The other schemes, with one exception, either cause the integration to blow up or to result in an obviously nonphysical simulation of the planetary boundary layer dynamics. The modified Level 2.5 model is proposed as a viable candidate for the prediction of turbulence and the simulation of the planetary boundary layer in general circulation models.