Finite-source filtering and Doppler modulation of infragravity waves generated by breakpoint forcing
Abstract
Infragravity waves generated in the surf zone contribute substantially to nearshore water-level variability, with group-scale variations in wave breaking generating free long waves through breakpoint forcing. Existing interpretations of this mechanism rely largely on an idealised moving-breakpoint picture in which breaking is tied to a local saturation relation, leaving unresolved how the finite extent and evolution of a realistic breaking region control the radiated waves. We first derive a local decomposition of the wave-induced forcing into breakpoint and bound wave forcing, separating the two contributions within the same evolving short-wave field. We then describe the breakpoint-forcing field as a finite, evolving source through its integrated strength, centroid, cross-shore width, and shape. This representation shows that finite source extent produces spatial interference, as phase differences between contributions emitted from different positions attenuate the high-frequency part of the infragravity response and shift this attenuation toward lower frequencies as the source widens. Source migration produces a directional Doppler shift by modifying the arrival times of successive emissions, with shoreward motion compressing arrivals at a shoreward observer and stretching them at a seaward observer. Breaking depth controls both the conversion of this forcing into surface elevation and the celerities governing these propagation-time effects. Controlled numerical experiments across a range of plane-beach slopes reproduce the predicted signatures: broader source footprints strengthen upper-band attenuation on both branches. The diagnosed migration history, with breaking strongest during shoreward motion, partly offsets that attenuation shoreward and reinforces it seaward.
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BibTeX
@misc{midouni2026finitesource,
title = {{Finite-source filtering and Doppler modulation of infragravity waves generated by breakpoint forcing}},
author = {Hedi Midouni and Stephanie Contardo and Jaak Monbaliu and Tomohiro Suzuki},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.03300},
eprint = {2609.03300},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.03300},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Finite-source filtering and Doppler modulation of infragravity waves generated by breakpoint forcing
AU - Hedi Midouni
AU - Stephanie Contardo
AU - Jaak Monbaliu
AU - Tomohiro Suzuki
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2609.03300
UR - https://arxiv.org/abs/2609.03300
AB - Infragravity waves generated in the surf zone contribute substantially to nearshore water-level variability, with group-scale variations in wave breaking generating free long waves through breakpoint forcing. Existing interpretations of this mechanism rely largely on an idealised moving-breakpoint picture in which breaking is tied to a local saturation relation, leaving unresolved how the finite extent and evolution of a realistic breaking region control the radiated waves. We first derive a local decomposition of the wave-induced forcing into breakpoint and bound wave forcing, separating the two contributions within the same evolving short-wave field. We then describe the breakpoint-forcing field as a finite, evolving source through its integrated strength, centroid, cross-shore width, and shape. This representation shows that finite source extent produces spatial interference, as phase differences between contributions emitted from different positions attenuate the high-frequency part of the infragravity response and shift this attenuation toward lower frequencies as the source widens. Source migration produces a directional Doppler shift by modifying the arrival times of successive emissions, with shoreward motion compressing arrivals at a shoreward observer and stretching them at a seaward observer. Breaking depth controls both the conversion of this forcing into surface elevation and the celerities governing these propagation-time effects. Controlled numerical experiments across a range of plane-beach slopes reproduce the predicted signatures: broader source footprints strengthen upper-band attenuation on both branches. The diagnosed migration history, with breaking strongest during shoreward motion, partly offsets that attenuation shoreward and reinforces it seaward.
ER -