Preferential orientation of floaters drifting in water waves

Abstract: Elongated floaters drifting in propagating water waves slowly rotate towards a preferential state of orientation. Short and heavy floaters tend to align longitudinally, along the direction of wave propagation, whereas long and light floaters align transversely, parallel to the wave crests and troughs. We investigate this phenomenon for homogeneous parallelepiped floaters by combining laboratory experiments with numerical simulations and asymptotic theory. For floaters small with respect to wavelength and for low amplitude waves, we show that the floater orientation is controlled by the non-dimensional number $F = k L_x^2 / \beta L_z$, with $k$ is the wavenumber, $\beta$ the floater-to-water density ratio, and $L_x$ and $L_z$ the floater length and thickness. Theory places the longitudinal-transverse transition at the critical value $F_c = 60$, in fair agreement with the experiments. Using a simplified physical model, we elucidate the physical origin of the preferential orientation. Through its motion, the floater probes the velocity gradients along its surface. Next to a small mean displacement (Stokes drift), this results in a net torque which, for short floaters, always favors the longitudinal orientation. This net torque arises from a phase correlation between the instantaneous buoyancy torque and the instantaneous yaw angle of the floater, a mechanism analogous to the Kapitza pendulum. The transverse equilibrium of longer floaters has a different origin and arises from the variation of the submersion depth along their long axis. This varying submersion significantly increases the torque in the trough positions, when the tips are more submersed, and always pushes towards the transverse orientation.