Novel theoretical and numerical results are presented on this important problem, which underlies current parametrization schemes for small-scale gravity waves in general circulation models. On the theoretical side, a very general framework has been constructed using the generalized Lagrangian-mean theory of wave--mean interaction. This novel framework allows a complete quantification of the mean vorticity transport due to dissipating gravity and/or sound waves. This includes, apparently for the first time, a general treatment of vorticity transport due to shock formation and other forms of wave breaking. The wave-induced vorticity transport is quantified within a complete and self-consistent set of equations for the mean potential vorticity, where ``mean'' stands for a Lagrangian (ie particle-following) average over the small-scale gravity waves.
On the numerical side, a shock-capturing finite-volume code is used to verify the predictions of the new theory in a shallow water model. This highlights the essential importance of using a momentum-conserving scheme to capture accurately the wave--mean interactions between gravity waves and larger-scale vortical motions. Many conventional numerical models would give wrong results here, even in the absence of wave breaking.
The results reported will be relevant for the improved design of gravity-wave parametrization schemes that seek to capture accurately the gravity-wave influence on the local (ie not just the zonally-averaged) mean flow.
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12th Conference on Atmospheric and Oceanic Fluid Dynamics