Growth rate and energy dissipation in wind-forced breaking waves

Abstract: We investigate the energy growth and dissipation of wind-forced breaking waves using direct numerical simulations of the coupled air-water Navier-Stokes equations. We vary the wind friction velocity over the wave speed $u_\ast/c$ up to 1. A turbulent wind boundary layer drives the growth of a pre-existing narrowband wave field until it breaks and transfers energy into the water column. Under sustained wind forcing, the wave field then resumes growth. We separately analyze energy transfers during wave growth and breaking-induced dissipation. Energy transfers are dominated by pressure input during growth and turbulent dissipation during breaking. The wave growth rate scales with $(u_\ast/c)^2$, modulated by the wave steepness due to sheltering. The energy dissipation follows the inertial scaling with wave slope at breaking, confirming the universality of the process. Following breaking, near-surface vertical turbulence dissipation profiles scale as $z^{-1}$, with its magnitude controlled by the breaking-induced dissipation.