  We advance our prior energy- and flux-budget turbulence closure model
(Zilitinkevich et al., 2007, 2008) for the stably stratified atmospheric flows
and extend it accounting for additional vertical flux of momentum and
additional productions of turbulent kinetic energy, turbulent potential energy
(TPE) and turbulent flux of potential temperature due to large-scale internal
gravity waves (IGW). Main effects of IGW are following: the maximal value of
the flux Richardson number (universal constant 0.2-0.25 in the no-IGW regime)
becomes strongly variable. In the vertically homogeneous stratification, it
increases with increasing wave energy and can even exceed 1. In the
heterogeneous stratification, when IGW propagate towards stronger
stratification, the maximal flux Richardson number decreases with increasing
wave energy, reaches zero and then becomes negative. In other words, the
vertical flux of potential temperature becomes counter-gradient. IGW also
reduce anisotropy of turbulence and increase the share of TPE in the turbulent
total energy. Depending on the direction (downward or upward), IGW either
strengthen or weaken the total vertical flux of momentum. Predictions from the
proposed model are consistent with available data from atmospheric and
laboratory experiments, direct numerical simulations and large-eddy
simulations.
