Boundary-driven Surface Wave Forces from a Self-propelling Vibrating Robot Boat

Active agents on fluid surfaces can perturb their surroundings by creating waves that reciprocally affect the agent. Inspired by the wave-mediated dynamics of surface-bouncing droplets, we study the motion and wave-field dynamics of a 6 cm radius, 9 cm tall, eccentric motor-driven vibrating robot boat on the surface of a 5 cm deep pool of water. The boat's vibration creates radially propagating gravity-capillary waves with frequency range 6-42 Hz and maximum amplitude 0.6 mm; a Schlieren method enables surface wave visualization with submillimeter resolution. The waves possess bow-stern and port-starboard symmetry, yielding a net-zero radiation force on the boat far from boundaries. When near a wall below a threshold distance, the boat's emitted waves interact with waves reflected off the boundary, creating a net field with reduced amplitude traveling toward the boundary. Meanwhile, waves emitted on the far side of the boat remain unchanged. Hence, the net wave force yields a boat-wall attraction, which we measure using the boat's displacement. Near the threshold, no reduced-amplitude field is born, and the boat experiences a slight repulsion. We observe the threshold to depend on wave frequency; a boat generating high-frequency waves will experience an attraction further from the wall than with low-frequency waves.