Wave drag due to generation of capillary-gravity surface waves

Abstract

The onset of the wave resistance via the generation of capillary-gravity waves by a small object moving with a velocity V is investigated experimentally. Due to the existence of a minimum phase velocity V(c) for surface waves, the problem is similar to the generation of rotons in superfluid helium near their minimum. In both cases, waves or rotons are produced at V>V(c) due to Cherenkov radiation. We find that the transition to the wave drag state is continuous: in the vicinity of the bifurcation the wave resistance force is proportional to sqrt[V-V(c)] for various fluids. This observation contradicts the theory of Raphaël and de Gennes. We also find that the reduced wave drag force for different fluids and different ball size may be scaled in such a way that all the data collapse on a single curve. The capillary-gravity wave pattern and the shape of the wave-generating region are investigated both experimentally and theoretically. Good agreement between the theory and the experimental data is found in this case.