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We advance our prior energy- and flux-budget turbulence closure model(Zilitinkevich et al., 2007, 2008) for the stably stratified atmospheric flowsand extend it accounting for additional vertical flux of momentum andadditional productions of turbulent kinetic energy, turbulent potential energy(TPE) and turbulent flux of potential temperature due to large-scale internalgravity waves (IGW). Main effects of IGW are following: the maximal value ofthe flux Richardson number (universal constant 0.2-0.25 in the no-IGW regime)becomes strongly variable. In the vertically homogeneous stratification, itincreases with increasing wave energy and can even exceed 1. In theheterogeneous stratification, when IGW propagate towards strongerstratification, the maximal flux Richardson number decreases with increasingwave energy, reaches zero and then becomes negative. In other words, thevertical flux of potential temperature becomes counter-gradient. IGW alsoreduce anisotropy of turbulence and increase the share of TPE in the turbulenttotal energy. Depending on the direction (downward or upward), IGW eitherstrengthen or weaken the total vertical flux of momentum. Predictions from theproposed model are consistent with available data from atmospheric andlaboratory experiments, direct numerical simulations and large-eddysimulations.

Energy- and flux-budget turbulence closure model for stably stratified flows. Part II: the role of internal gravity waves