Preferential orientation of small floaters drifting in water waves

Abstract

Elongated floaters drifting in propagating water waves slowly rotate towards a preferential orientation with respect to the direction of incidence. In this article, we study this phenomenon in the small-floater limit $k L_x < 1 $, with $k$ the wavenumber and $L_x$ the floater length. Experiments show that short and heavy floaters tend to align longitudinally, along the direction of wave propagation, whereas longer and lighter floaters align transversely, parallel to the wave crests and troughs. We show that this preferential orientation can be modeled using an inviscid Froude-Krylov model, ignoring diffraction effects. Asymptotic theory, in the double limit of small wave slope and small floater, suggests that preferential orientation is essentially controlled by the non-dimensional number $F = k L_x^2 / \overline{h}$, with $\overline{h}$ the equilibrium submersion depth. Theory predicts the longitudinal-transverse transition {for homogeneous parallelepipeds} at the critical value $F_c = 60$, in fair agreement with the experiments that locate $F_c = 50 \pm 15$. Using a simplified model for a thin floater, we elucidate the physical mechanisms that control the preferential orientation. The longitudinal equilibrium for $F<F_c$ originates from a slight asymmetry between the buoyancy torque induced by the wave crests, that favors the longitudinal orientation, and that induced by the wave troughs, that favors the transverse orientation. The transverse equilibrium for $F>F_c$ arises from the variation of the submersion depth along the long axis of the floaters, which significantly increases the torque in the trough positions, when the tips are more submersed.