On the limiting geometry of unsteady breaking waves subject to co-flowing wind: spectrally-informed versus locally-measured steepness
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| Format: | Preprint |
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2026
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| _version_ | 1866917540888838144 |
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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 |
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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 |