Spatio-Temporal Analysis of Surface Waves Generating Octupole Vortices in a Square Domain

Abstract

In this study, we examine the underlying surface wave dynamics forming an octupole structure of vortices on the air–water interface. The surface waves are generated by a square wavemaker made of four cylindrical edges half-submerged on the interface. These waves direct the motion of floaters into gyrating trajectories, forming two counter-rotating vortices along each edge of the wavemaker and generating the overall octupole pattern. We 3D reconstruct the wave heights and describe the underlying flow through spatio-temporal analysis. Specifically, we decompose the overall wave field into components coming from the edges and corners of the wavemaker. To our knowledge, we are first to obtain a closed-form solution for a velocity potential, via a superposition of edge and phase-shifted oblique progressive waves produced by the wavemaker, to qualitatively model these octupole vortices. The methodology outlined provides a phenomenological approach to characterize the flow that may be useful for characterizing waves inside arbitrary finite-sized domains.