Echolocation Through Gravity-Capillary Waves

We present a theoretical model for the radiation and scattering of gravity-capillary waves produced by small insects, represented as an oscillating disk. We derive a solution for the radiated waves along with their added mass and damping relations. The solution for the scattering behavior of these waves off a fixed object on the surface is also described. This model builds upon existing gravity-wave solutions with a modification to the condition on the free surface. These models were compared against results produced in a mechanical wave-maker whose surface topography was measured using the free-surface synthetic Schlieren method. From these models we provide insight into how objects on the free-surface may be sensed remotely.