Title: The energetic inception of breaking in surface gravity waves under wind forcing

Abstract: The breaking of surface gravity waves is a key process contributing to air-sea fluxes and turbulent ocean mixing. The highly nonlinear nature of wave breaking, combined with the challenges of observing this process in a laboratory or field setting, leaves our understanding of the energetic processes underpinning wave breaking incomplete. Progress towards refining this understanding was made in a recent study (D. G. Boettger et. al., An energetic signature for breaking inception in surface gravity waves, Journal of Fluid Mechanics 959, A33 (2023)), which identified an energetic signature in the wave kinetic energy evolution that preceded breaking onset and correlated with the strength of the breaking event. In this study, we examine the influence of wind forcing on this energetic signature. We develop a numerical wave tank that simulates wind flowing over mechanically generated waves and construct an ensemble of cases with varying wave steepness and wind forcing speed. The wind is shown to modulate the wave geometry and elevate kinetic energy at crest tip by up to 35 %. Despite these influences, the energetic inception signature was found to robustly indicate breaking inception in all cases examined, with a threshold value in the kinetic energy growth rate at this instant separating breaking and non-breaking waves. Under wind forcing, the timing of the energetic inception point occurred slightly earlier that unforced breaking waves, giving advance warning of breaking 0.3 wave periods prior to breaking onset.