A Multi-Scale Theory for Gravity-Wave Interaction with Turbulence

The interaction between small-scale waves and a larger-scale flow can be described by a multi-scale theory that forms the basis for parameterizations of subgrid-scale gravity waves (GWs) in weather and climate models (e.g., Achatz et al., 2023). These parameterizations have recently been extended to include transient GW–mean-flow interactions and oblique GW propagation. Existing gravity-wave parameterizations include only rudimentary descriptions of the coupling between the dynamics of unresolved GWs and turbulence, but recent studies (Banerjee et al., 2025) have shown that this interaction is non-negligible. Energetic consistency therefore necessitates an extension of the multi-scale theory to include a more accurate representation of this interaction.

We propose an extension of this multi-scale theory that incorporates an additional turbulence formulation, allowing for a more robust bidirectional coupling between GWs and turbulence. Key results include a well-defined organization of turbulence along the phase structure of individual GWs and a correspondingly structured feedback on turbulent GW damping. We plan to present initial results from the validation of this extended theory by comparing idealized simulations with parameterized GWs to wave-resolving reference simulations.