Capillary-Gravity Waves Generated by a Sudden Object Motion

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.