The process of breaking in surface gravity waves can be characterized by two distinct stages. Breaking onset is defined as the first visible surface manifestation of breaking. This is preceded by breaking inception, which is characterized by the initiation of an irreversible process within the crest that inevitably leads to breaking. Breaking inception diagnostics formulated using the local energetic, kinematic, and geometric properties of the wave crest have recently been proposed that appear to provide generic parametric threshold estimates and may facilitate the effect of wave breaking on larger-scale processes to be parametrized. In a recent numerical study [McAllister et al., J. Fluid Mech. 974, A14 (2023)], a breaking inception diagnostic was proposed based on a threshold value for the maximum local interface angle $\mathrm{\Theta }$. Utlizing an ensemble of breaking wave packet numerical simulations, we extend these findings to include surface tension effects, which are an inescapable feature of ocean surface waves and are known to have a non-negligible effect on wave geometry. The ensemble consists of narrow bandwidth, short wavelength $(\sim 1\mathrm{m})$ gravity wave packets with varying packet size, water depth, and wind speed forcing. For this data, we show that ${\mathrm{\Theta }}_{\text{th}}={60}^{\circ }$ is a robust threshold value for the initiation of breaking inception; twice the magnitude of that for waves in the absence of surface tension. We explore this result in the context of the kinematic inception parameter $B$ [Barthelemy et al., J. Fluid Mech. 841, 463 (2018)] and show that the kinematic and geometric methods are related through the relative flux of energy into the wave crest.

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• Surface gravity waves
• Wave breaking
• Nonlinear waves