Capillary effects on preferential orientation of floaters in gravity waves

Abstract

We study the influence of capillary effects on the motion of thin elastic plates denser than water drifting in propagating surface gravity waves. Such floaters experience a mean angular drift that rotates them toward two preferential orientations: parallel to the direction of wave propagation (longitudinal) or parallel to the wave crests (transverse). We develop a diffractionless model (Froude-Krylov approximation) to compute the mean yaw moment acting on floaters with arbitrary bending rigidity, small relative to the wavelength. Capillary forces are incorporated through a quasi-static volume formulation based on the fluid volume displaced by the floater and its meniscus. The model predicts that the preferential orientation is governed by the non-dimensional parameter $F = kL_x^2/\overline{h}$ recently introduced in Herreman et al. (J. Fluid Mech., vol.999, 2024, A92), where $k$ is the wavenumber, $L_x$ the floater length, and $\overline{h}$ the equilibrium immersion depth, provided that $\overline{h}$ accounts for capillary effects. The orientation depends on how $F$ compares to a critical value $F_c$, which is a function of the ratio of the flexural length to the floater length. These predictions are in good agreement with experiments performed with thin metal rectangular plates of various length, width and thickness.