A representative underlying scale for spectrally-resolved energy dissipation in surface breaking waves
Author(s)
Cao, Rui
Padilla, Enrique
Chen, Xu
Callaghan, Adrian
Type
Journal Article
Abstract
In the Duncan-Phillips framework for breaking wave energy dissipation, the underlying scale at which dissipation occurs is commonly inferred from a measure of the breaking-wave phase speed, most often taken as the spectrally-informed phase speed(Cs), the local phase
speed at incipient breaking (Cb), and the white cap advancing speed(Cw). However, energy loss occurs across a finite spectral band, and the link between these single-speed measures and the representative dissipation scale requires further investigation. Using unidirectional laboratory wavegroups, we identify the spectral range over which energy dissipation occurs in breaking waves (≈0.95fp-1.8fp, with fp the peak frequency). From this, we define an energy-dissipation-weighted frequency fΥ and a corresponding phase speed CΥ(via the linear dispersion relation), which characterise the effective scale at which energy is lost from the wave group. We show that for the waves studied here this dissipative scale is systematically smaller than local and spectral speed measures, with CΥ≃O(0.95Cb)≃ 27O(0.87Cs). When inferred from whitecap-based measures (most commonly implemented
in the field from optical remote sensing),CΥcorresponds to approximately O(0.91-0.96) of the time-averaged white cap advancing speed, depending on how the whitecap speed
is defined. Taken together, these correlations indicate that the commonly used measures Cs,Cb, and white cap-based speeds are broadly connected, with our quantitative analysis further demonstrating that their relationships are modulated by the strength of breaking. Overall, our study provides a clearer physical basis for identifying dissipation scales in broadband breaking waves and helps reconcile existing laboratory, numerical, and field-based approaches.
speed at incipient breaking (Cb), and the white cap advancing speed(Cw). However, energy loss occurs across a finite spectral band, and the link between these single-speed measures and the representative dissipation scale requires further investigation. Using unidirectional laboratory wavegroups, we identify the spectral range over which energy dissipation occurs in breaking waves (≈0.95fp-1.8fp, with fp the peak frequency). From this, we define an energy-dissipation-weighted frequency fΥ and a corresponding phase speed CΥ(via the linear dispersion relation), which characterise the effective scale at which energy is lost from the wave group. We show that for the waves studied here this dissipative scale is systematically smaller than local and spectral speed measures, with CΥ≃O(0.95Cb)≃ 27O(0.87Cs). When inferred from whitecap-based measures (most commonly implemented
in the field from optical remote sensing),CΥcorresponds to approximately O(0.91-0.96) of the time-averaged white cap advancing speed, depending on how the whitecap speed
is defined. Taken together, these correlations indicate that the commonly used measures Cs,Cb, and white cap-based speeds are broadly connected, with our quantitative analysis further demonstrating that their relationships are modulated by the strength of breaking. Overall, our study provides a clearer physical basis for identifying dissipation scales in broadband breaking waves and helps reconcile existing laboratory, numerical, and field-based approaches.
Date Issued
2026-04-01
Date Acceptance
2026-03-30
Citation
Journal of Geophysical Research (JGR): Oceans, 2026, 131 (4)
ISSN
2169-9275
Publisher
American Geophysical Union
Journal / Book Title
Journal of Geophysical Research (JGR): Oceans
Volume
131
Issue
4
Copyright Statement
© 2026. The Author(s). This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
License URL
Identifier
10.1029/2025JC023904
Publication Status
Published
Article Number
e2025JC023904
Date Publish Online
2026-04-16