  The interaction between small-scale waves and a larger-scale flow can be
described by a multi-scale theory that forms the basis for a new class of
parameterizations of subgrid-scale gravity waves (GW) in weather and climate
models. The development of this theory is reviewed here. It applies to all
interesting regimes of atmospheric stratification, i.e. also to moderately
strong stratification as occurring in the middle atmosphere, and thereby
extends classic assumptions for the derivation of quasi-geostrophic theory. At
strong wave amplitudes a fully nonlinear theory arises that is complemented by
a quasilinear theory for weak GW amplitudes. The latter allows the extension to
a spectral description that forms the basis of numerical implementations that
avoid instabilities due to caustics, e.g. from GW reflection. Conservation
properties are discussed, for energy and potential vorticity, as well as
conditions under which a GW impact on the larger-scale flow is possible. The
numerical implementation of the theory for GW parameterizations in atmospheric
models is described, and the consequences of the approach are discussed, as
compared to classic GW parameterizations. Although more costly than the latter,
it exhibits significantly enhanced realism, while being considerably more
efficient than an approach where all relevant GWs are to be resolved. The
reported theory and its implementation might be of interest also for the
efficient and conceptually insightful description of other wave-mean
interactions, including those where the formation of caustics presents a
special challenge.
