Theoretical modeling of surfers on a vibrating bath*

We present a theoretical investigation into the dynamics of capillary-scale objects surfing on their own self-generated wave field. Our study is motivated by a newly discovered system consisting of superhydrophobic objects floating on a vertically vibrating fluid bath. Experiments have demonstrated that such ``surfers" propagate along the fluid interface, and that multiple surfers may self-organize through their wave-induced interactions. Our theoretical model consists of coupled equations for the surfers' positional and orientational dynamics, in which a surfer is modeled as a source of capillary waves. The model predictions exhibit good agreement with experimentally observed interaction modes between two surfers. Generally, this work shows that the surfer system is amenable to quantitative theoretical modeling, and thus constitutes a promising platform for constructing and validating new theories of interfacial active matter.