2026 Gallet Surface Gravity Wave Mean Flow

In this study, we investigate the interaction between narrow-band deep-water surface gravity waves and a background flow with comparable spatial scales, focusing on the scenario where the background flow speed aligns with the Stokes drift of the waves. The objective is to derive a comprehensive two-way coupled model that reflects both the fast wave dynamics and the slower background flow. The methodology involves integrating nonlinear wave interactions into the derivation, resulting in a nonlinear version of the reduced wave equation, coupled with a Craik-Leibovich equation governing the background flow evolution. This coupled model allows for the description of wave and flow dynamics over the slow turnover frequency of the background flow, significantly reducing computational demands associated with resolving fast wave frequencies. Notably, the inviscid model conserves key physical quantities such as wave action, mechanical energy, and horizontal momentum, while the viscous version preserves horizontal momentum. Furthermore, the model presents coupling terms in a compact form, facilitating both physical interpretation and numerical implementation. The findings provide valuable insights into the complexities of wave-mean flow interactions in oceanic environments.