Growth rate and energy dissipation in wind-forced breaking waves

TL;DR

This study uses direct numerical simulations to analyze how wind-driven breaking waves grow and dissipate energy, revealing universal scaling laws and detailed energy transfer mechanisms during wave evolution.

Contribution

It provides new insights into the energy transfer processes and scaling laws governing wind-forced breaking waves through high-fidelity simulations.

Findings

Wave growth rate scales with (u_*/c)^2

Energy dissipation during breaking follows inertial scaling with wave slope

Near-surface turbulence dissipation scales as z^{-1} after breaking

Abstract

We investigate the energy growth and dissipation of wind-forced breaking waves at high wind speed using direct numerical simulations of the coupled air-water Navier-Stokes equations. A turbulent wind boundary layer drives the growth of a pre-existing narrowband wave field until it breaks, transferring energy into the water column. Under sustained wind forcing, the wave field 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. Wind input during growth is balanced with dissipation during breaking over an entire growing-breaking cycle. The wave growth rate scales with $(u_\ast/c)^2$, modulated by the wave steepness due to sheltering, and 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 their magnitude controlled by the breaking-induced dissipation.