Thermal effects of saturating gravity waves in the atmosphere

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Abstract
Breaking/saturating gravity waves (GWs) not only exert drag on the mean flow due to their momentum deposition but also affect the background thermally because of the associated energy flux divergence. We present a rigorous derivation of terms describing the thermal effects of GWs on the mean flow, based on the corresponding energy cycle for wave/mean flow interactions. The combined effect of saturating GWs is to produce both differential heating and cooling by inducing a downward wave heat flux, and an irreversible conversion of wave energy into heat. The former effect can also be represented as thermal diffusion acting on the mean potential temperature gradient. This rigorous theory for the thermal exchange between waves and the mean flow can be closed once the mechanism for GW dissipation is parameterized. To illustrate the procedure, we employ our recent nonlinear theory of GW spectra to derive expressions for the wave‐induced heating rates. This yields a parameterization of the thermal effects of GWs, which is suitable for use in general circulation models and requires the source GW spectrum as the only tunable parameter. We present results of numerical calculations of wave heating terms for typical wind and temperature profiles as well as simulations with the full‐scale Canadian Middle Atmosphere Model (CMAM).