Axisymmetric radiation and decay of gravity-capillary waves

Some centimeter-scale water surface bound aquatic insects employ echolocation in search of food, allies, and predators by generating and detecting free surface waves. We present a combined theoretical and experimental study of gravity-capillary waves, which are generated by a disk oscillating vertically about the horizontal free surface. The radiated waves are predicted using matched eigenfunction expansions, as employed in existing models of surface gravity waves. Here we account for surface tension and viscosity to investigate the effects of oscillating a small object on the water surface. Our model was tested against experiments in which the surface topography of waves ranging from 10 to 100 Hz were measured using the free-surface synthetic Schlieren method. Although a small amount of viscosity has minor effects on the dispersion relation and the wavelength of the surface waves, it has long range influence on the amplitude of the surface elevation. Our findings show that surface waves around small floating objects are significantly dampened by viscosity.