Viscous decay of gravity-capillary waves around an oscillating body

Small organisms and objects on the order of centimeters produce gravity-capillary waves on the water surface, which could be exploited for sensing and communication. The rate of dissipation of the interfacial waves is a key limiting factor that is not fully understood. We present a theoretical and experimental study of circular waves radiating and decaying from an oscillating disk. The theory accounts for viscosity and reproduces the same classical result as the exact dispersion relation derived by Lamb. The predictions are compared with surface elevation data measured using the synthetic Schlieren method and a more accurate, confocal displacement sensor. Our results show that interfacial waves decay at a rate that increases linearly with oscillation frequency as predicted, but the measured waves decay more quickly with distance than expected. The findings may serve as a foundation for studying the range of perception and communication by various organisms on the water surface.