Vortex lattice state transitions in water surface waves

Abstract

Surface waves can generate an ordered vortex lattice of fluid particles on the air-water interface. Here, the transitions of the lattice structure are observed through experiments and modelled analytically. A fully-immersed square waveguide system is positioned at the center of a larger bath which directs particles into counter-rotating vortices. Flow interactions with the bath free-surface alter the ordered structure, and a state transition is initiated by the increase of the waveguide immersion depth. It manifests as a change in the orbital momentum and spin properties of the vortices, and develops through the combination of reflected-wave attenuation and mean flow effects from the classical Stokes drift and Eulerian currents. Transitions from a perfect antiferromagnetic state to weakly-ordered ones are achieved, including a monopole vortex reminiscent of spectral condensates in thin fluid layers. Order in the disordered flow is uncovered through velocity field corrections after invoking time-scale separation. The lattice structures are modelled analytically through a superposition of mean flow contributions from the waveguide and bath modes. The results open a new platform for investigating the dynamics of wave and vortex lattice interactions, and devising new techniques to characterize complex flow phenomena on the air-water interface.