Capillary-Gravity Waves Generated by a Sudden Object Motion

TL;DR

This paper provides a theoretical analysis of capillary-gravity waves generated by sudden object motions on water, revealing nonzero wave resistance even below the minimum phase velocity, with implications for water-walking insects.

Contribution

It introduces a new theoretical framework for understanding transient wave resistance caused by sudden object accelerations or decelerations on water.

Findings

Wave resistance remains nonzero below $c_{min}$ during sudden motions.

Transient wave patterns differ from steady-state waves.

Results may inform studies of water-walking insects' propulsion.

Abstract

We study theoretically the capillary-gravity waves created at the water-air interface by a small object during a sudden accelerated or decelerated rectilinear motion. We analyze the wave resistance corresponding to the transient wave pattern and show that it is nonzero even if the involved velocity (the final one in the accelerated case, the initial one in the decelerated case) is smaller than the minimum phase velocity $c_{min}=23 \mathrm{cm s^{-1}}$. These results might be important for a better understanding of the propulsion of water-walking insects where accelerated and decelerated motions frequently occur.