Capillary-gravity wave resistance of a translating, pulsating source
Abstract
A disturbance in steady rectilinear translation along a capillary-gravity interface radiates waves only above a minimum speed cmin, where it experiences a wave resistance; below this threshold it generates no waves, and the response is merely a localised deformation of the interface around the source, free of wave resistance. Modulating the source amplitude at a frequency Ω shifts the forcing to the sideband pair kV±Ω, where k is the wavenumber and V is the translation speed, opening resonance conditions absent from the steady problem; radiation then sets in below the steady threshold cmin. Here we derive the mean wave resistance ⟨ R⟩ of a line source in closed form, and show it to be strictly positive at every nonzero speed V: the drag-free below-threshold regime disappears for any Ω≠ 0. Crossing the radiation transitions---where the group velocity matches the source speed---produces integrable resonant peaks in ⟨ R⟩, whose exponents we derive, including at the cusp where two transition branches merge. Below threshold, where a steadily moving source feels no drag, ⟨ R⟩ rises from zero as Ω5 (at fixed V). Throughout, surface tension is essential to ⟨ R⟩: because it controls the short, dominant capillary-scale waves, discarding it misrepresents ⟨ R⟩ over almost the entire speed-frequency plane.
Versions
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BibTeX
@misc{diamant2026capillarygravity,
title = {{Capillary-gravity wave resistance of a translating, pulsating source}},
author = {Haim Diamant and Elie Raphael},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15859},
eprint = {2610.15859},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15859},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Capillary-gravity wave resistance of a translating, pulsating source
AU - Haim Diamant
AU - Elie Raphael
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15859
UR - https://arxiv.org/abs/2610.15859
AB - A disturbance in steady rectilinear translation along a capillary-gravity interface radiates waves only above a minimum speed c_min, where it experiences a wave resistance; below this threshold it generates no waves, and the response is merely a localised deformation of the interface around the source, free of wave resistance. Modulating the source amplitude at a frequency Ω shifts the forcing to the sideband pair kV±Ω, where k is the wavenumber and V is the translation speed, opening resonance conditions absent from the steady problem; radiation then sets in below the steady threshold c_min. Here we derive the mean wave resistance ⟨ R⟩ of a line source in closed form, and show it to be strictly positive at every nonzero speed V: the drag-free below-threshold regime disappears for any Ω≠ 0. Crossing the radiation transitions---where the group velocity matches the source speed---produces integrable resonant peaks in ⟨ R⟩, whose exponents we derive, including at the cusp where two transition branches merge. Below threshold, where a steadily moving source feels no drag, ⟨ R⟩ rises from zero as Ω^5 (at fixed V). Throughout, surface tension is essential to ⟨ R⟩: because it controls the short, dominant capillary-scale waves, discarding it misrepresents ⟨ R⟩ over almost the entire speed-frequency plane.
ER -