Momentum fluxes in wind-forced breaking waves

Abstract

We investigate the momentum fluxes between a turbulent air boundary layer and a growing-breaking wave field by solving the air-water two-phase Navier-Stokes equations through direct numerical simulations (DNS). A fully-developed turbulent airflow drives the growth of a narrowbanded wave field, whose amplitude increases until reaching breaking conditions. The breaking events result in a loss of wave energy, transferred to the water column, followed by renewed growth under wind forcing. We revisit the momentum flux analysis in a high-wind speed regime, characterized by the ratio of the friction velocity to wave speed $u_\ast/c$ in the range $[0.3-0.9]$, through the lens of growing-breaking cycles. The total momentum flux across the interface is dominated by pressure, which increases with $u_\ast/c$ during growth and reduces sharply during breaking. Drag reduction during breaking is linked to airflow separation, a sudden acceleration of the flow, an upward shift of the mean streamwise velocity profile, and a reduction in Reynolds shear stress. We characterize the reduction of pressure stress and flow acceleration through an aerodynamic drag coefficient by splitting the analysis between growing and breaking stages, treating them as separate sub-processes. While drag increases with $u_\ast/c$ during growth, it drops during breaking. Averaging over both stages leads to a saturation of the drag coefficient at high $u_\ast/c$, comparable to what is observed at high wind speeds in laboratory and field conditions. Our analysis suggests this saturation is controlled by breaking dynamics.