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Peer-reviewedCC BY 4.0Journal of Fluid Mechanics

Swallowtail catastrophes in supercritical capillary-gravity wakes generated by unsteady motion

  • Johann Herault
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Abstract

Surface-swimming animals generate capillary-gravity waves whose patterns reflect the unsteady, sinuous nature of their trajectories. For uniform circular motion, cusp formation and wavefront folding have been observed at supercritical speeds. Here, we show that slaloming trajectories at supercritical speeds produce wavefront singularities of higher codimension than previously reported, namely a swallowtail catastrophe. Combining observations of surface-swimming snakes with numerical simulations of unsteady wakes, we identify a swallowtail catastrophe embedded in the wave envelope. This is explained by an integral formulation with a delay term accounting for the timing of wave emission along the trajectory, enabling a description of singularity formation and degeneracy within catastrophe theory. These results provide a general framework for predicting the emergence of caustics and cusps in wavefronts generated by unsteady motions.

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Cite

BibTeXRIS
BibTeX
@article{herault2026swallowtail,
  title = {{Swallowtail catastrophes in supercritical capillary-gravity wakes generated by unsteady motion}},
  author = {Johann Herault},
  journal = {Journal of Fluid Mechanics},
  year = {2026},
  month = aug,
  doi = {10.1017/jfm.2026.11888},
  url = {https://hal.science/hal-05770535v1},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Swallowtail catastrophes in supercritical capillary-gravity wakes generated by unsteady motion
AU  - Johann Herault
PY  - 2026
DA  - 2026/08/28
JO  - Journal of Fluid Mechanics
DO  - 10.1017/jfm.2026.11888
UR  - https://hal.science/hal-05770535v1
AB  - Surface-swimming animals generate capillary-gravity waves whose patterns reflect the unsteady, sinuous nature of their trajectories. For uniform circular motion, cusp formation and wavefront folding have been observed at supercritical speeds. Here, we show that slaloming trajectories at supercritical speeds produce wavefront singularities of higher codimension than previously reported, namely a swallowtail catastrophe. Combining observations of surface-swimming snakes with numerical simulations of unsteady wakes, we identify a swallowtail catastrophe embedded in the wave envelope. This is explained by an integral formulation with a delay term accounting for the timing of wave emission along the trajectory, enabling a description of singularity formation and degeneracy within catastrophe theory. These results provide a general framework for predicting the emergence of caustics and cusps in wavefronts generated by unsteady motions.
SN  - 0022-1120
SN  - 1469-7645
ER  -