Multi-Scale Dynamics of the Interaction Between Waves and Mean Flows: From Nonlinear WKB Theory to Gravity-Wave Parameterizations in Weather and Climate Models

TL;DR

This paper reviews a multi-scale nonlinear theory of wave-mean flow interactions, extending classic assumptions, and develops a new gravity wave parameterization for weather and climate models that improves realism and efficiency.

Contribution

It introduces a comprehensive multi-scale nonlinear theory for wave-mean flow interactions applicable across stratification regimes, and presents a novel gravity wave parameterization for atmospheric models.

Findings

The theory applies to all stratification regimes, including moderate and strong stratification.

The nonlinear and quasilinear formulations enable stable spectral numerical implementations.

The new parameterization enhances realism in models while maintaining computational efficiency.

Abstract

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.