On the limiting geometry of unsteady breaking waves subject to co-flowing wind: spectrally-informed versus locally-measured steepness

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Main Authors: Cao, Rui, Padilla, Enrique M., Chen, Xu, Callaghan, Adrian H.
Format: Preprint
Published: 2026
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author Cao, Rui
Padilla, Enrique M.
Chen, Xu
Callaghan, Adrian H.
author_facet Cao, Rui
Padilla, Enrique M.
Chen, Xu
Callaghan, Adrian H.
contents Wave steepness is a key geometric variable for describing breaking occurrence and its consequences, including energy dissipation and air entrainment. Using three laboratory campaigns under varying spectral conditions and co-flowing wind forcing, we contrast two types of steepness commonly used for unsteady breaking waves: spectrally-informed wave-group steepness (prognostic), obtained from fixed-point surface-elevation records, and locally-measured crest steepness (diagnostic), obtained from spatial surface profiles extracted using the SDBW-I image-processing method developed herein. For the former, the long-adopted $\mathcal{S}_n$ (linear sum of Fourier-component steepness) increases appreciably within about two dominant wavelengths upstream of breaking because of its sensitivity to evolving high-frequency content. When measured sufficiently far upstream, however, wave-group steepness remains approximately linearly related to the local zero-crossing steepness $\mathcal{S}_b$ across bulk unforced conditions. Notwithstanding this, we argue that the crest-front steepness, $\mathcal{S}_{\mathrm{front}}(t_b)$, which delineates the front-face slope at incipient breaking, is the most physically meaningful metric examined here. It exhibits a consistent breaking-onset lower-bound threshold of $\mathcal{S}_{\mathrm{front}}(t_b)\approx0.2$, while values above this threshold decrease with wind speed as crests become less forward leaning. This may be attributed to wind-modified dispersion, enhanced high-frequency spectral content and aerodynamic sheltering, suggesting that wind--wave and wave--wave interactions act as competing mechanisms in triggering breaking through kinematic and energetic processes beyond what geometry alone can explain. Even so, $\mathcal{S}_{\mathrm{front}}(t_b)$ has strong potential as a controlling variable for future studies of breaking energetics and crest-scale dynamics.
format Preprint
id arxiv_https___arxiv_org_abs_2605_28907
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle On the limiting geometry of unsteady breaking waves subject to co-flowing wind: spectrally-informed versus locally-measured steepness
Cao, Rui
Padilla, Enrique M.
Chen, Xu
Callaghan, Adrian H.
Fluid Dynamics
Atmospheric and Oceanic Physics
Wave steepness is a key geometric variable for describing breaking occurrence and its consequences, including energy dissipation and air entrainment. Using three laboratory campaigns under varying spectral conditions and co-flowing wind forcing, we contrast two types of steepness commonly used for unsteady breaking waves: spectrally-informed wave-group steepness (prognostic), obtained from fixed-point surface-elevation records, and locally-measured crest steepness (diagnostic), obtained from spatial surface profiles extracted using the SDBW-I image-processing method developed herein. For the former, the long-adopted $\mathcal{S}_n$ (linear sum of Fourier-component steepness) increases appreciably within about two dominant wavelengths upstream of breaking because of its sensitivity to evolving high-frequency content. When measured sufficiently far upstream, however, wave-group steepness remains approximately linearly related to the local zero-crossing steepness $\mathcal{S}_b$ across bulk unforced conditions. Notwithstanding this, we argue that the crest-front steepness, $\mathcal{S}_{\mathrm{front}}(t_b)$, which delineates the front-face slope at incipient breaking, is the most physically meaningful metric examined here. It exhibits a consistent breaking-onset lower-bound threshold of $\mathcal{S}_{\mathrm{front}}(t_b)\approx0.2$, while values above this threshold decrease with wind speed as crests become less forward leaning. This may be attributed to wind-modified dispersion, enhanced high-frequency spectral content and aerodynamic sheltering, suggesting that wind--wave and wave--wave interactions act as competing mechanisms in triggering breaking through kinematic and energetic processes beyond what geometry alone can explain. Even so, $\mathcal{S}_{\mathrm{front}}(t_b)$ has strong potential as a controlling variable for future studies of breaking energetics and crest-scale dynamics.
title On the limiting geometry of unsteady breaking waves subject to co-flowing wind: spectrally-informed versus locally-measured steepness
topic Fluid Dynamics
Atmospheric and Oceanic Physics
url https://arxiv.org/abs/2605.28907