Momentum and energy fluxes in wind-forced breaking waves at high wind speeds*

We perform direct numerical simulations (DNS) of wind-forced breaking waves by solving the two-phase Navier-Stokes equations. The turbulent upper airflow drives the growth of a narrowband wave field, with wave amplitude increasing until breaking occurs. After the breaking stage, the waves continue to grow under wind forcing. We examine these cycles in the high-wind speed regime, characterized by the ratio of friction velocity to wave speed $u_\ast/c$ in the range [0.3−0.9]. We analyze the momentum and energy fluxes exchanged among the airflow, wave field, and water currents. The total momentum flux is mainly governed by the pressure contribution, which increases with $u_\ast/c$ in the pre-breaking stage and suddenly reduces during breaking stage. These effects balance, leading to a saturation of the pressure force over a breaking cycle, similar to the drag force saturation at high wind speeds observed in experiments and fields observations. The water column's energy budget shows the pressure input's dominance during wave growth and dissipation during breaking. These observations align with scaling laws for wave growth [1] and breaking-induced dissipation [2].

[1] Miles J. "On the generation of surface waves by shear flows." Journal of Fluid Mechanics 3.2 (1957): 185-204.

[2] Drazen D. et al. "Inertial scaling of dissipation in unsteady breaking waves." Journal of fluid mechanics 611 (2008): 307-332.