Shape considerations in wave-driven propulsion
Abstract
At the fluid surface, an asymmetric wave field generated by an oscillating body produces thrust in what is known as wave-driven propulsion (WDP). Although this thrust is directed forward, the vertical oscillations inevitably produce waves radiating outwards in all directions. The effect of these side waves is not accounted for in simplified models focused on the fore--aft wave field. In this work, we take a two-dimensional shallow water approach, deriving thrust and power expressions that account for surface waves emitted in any direction. Supported by an analytically driven approach, we pose a numerical optimisation problem to maximise thrust, imposing appropriate Sommerfeld boundary conditions across subcritical and supercritical velocity regimes. The two-dimensional set-up allows us to understand how the side waves emitted by the body contribute to thrust and efficiency. Furthermore, we explore how maximal thrust depends on the shape of the body beginning with a square followed by ellipses of varying aspect ratios. Using these learnings, we include the shape of the body as a control variable to demonstrate how an optimised shape can lead to further thrust and efficiency gains.
Related
- Wave-driven propulsion of a flexible raft
- Harmonics of femtosecond and continuous-wave radiation for precision spectroscopy: generation efficiency and spectral line shape
- Ambient Pressure-Driven Actuators and Shape-Morphing Metamaterials
- Wave-driven contraction-deformation coupling enables the motility and revolving waves of active gel droplets
- Shape Transformations and Rupture of a Vesicle Driven by an Encapsulated Active Particle
BibTeX
@misc{odonovan2026shape,
title = {{Shape considerations in wave-driven propulsion}},
author = {Daire O'Donovan and Graham P. Benham},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.18422},
eprint = {2609.18422},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.18422},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Shape considerations in wave-driven propulsion
AU - Daire O'Donovan
AU - Graham P. Benham
PY - 2026
DA - 2026/09/16
PB - arXiv
DO - 10.48550/arxiv.2609.18422
UR - https://arxiv.org/abs/2609.18422
AB - At the fluid surface, an asymmetric wave field generated by an oscillating body produces thrust in what is known as wave-driven propulsion (WDP). Although this thrust is directed forward, the vertical oscillations inevitably produce waves radiating outwards in all directions. The effect of these side waves is not accounted for in simplified models focused on the fore--aft wave field. In this work, we take a two-dimensional shallow water approach, deriving thrust and power expressions that account for surface waves emitted in any direction. Supported by an analytically driven approach, we pose a numerical optimisation problem to maximise thrust, imposing appropriate Sommerfeld boundary conditions across subcritical and supercritical velocity regimes. The two-dimensional set-up allows us to understand how the side waves emitted by the body contribute to thrust and efficiency. Furthermore, we explore how maximal thrust depends on the shape of the body beginning with a square followed by ellipses of varying aspect ratios. Using these learnings, we include the shape of the body as a control variable to demonstrate how an optimised shape can lead to further thrust and efficiency gains.
ER -