Transport and orientation of anisotropic particles settling in surface gravity waves

TL;DR

This study investigates how anisotropic particles settle and orient in surface gravity waves, revealing how their equilibrium orientation and horizontal transport depend on settling speed, wave parameters, and finite-size effects.

Contribution

It introduces a comprehensive analysis of the coupled translation and orientation dynamics of anisotropic particles in waves, including inertial torque effects and finite-size considerations.

Findings

Inertial torque causes broadside alignment of particles.

Transition from aspect ratio-dependent to initial-condition-dependent orientation.

Finite-size effects influence particle drift, validating the finite-size approximation.

Abstract

We study the translation and orientation dynamics of an anisotropic particle settling in monochromatic linear surface gravity waves. Recent work has shown that a neutrally buoyant spheroid attains a preferred mean orientation in such wave fields, independent of its initial state and determined solely by its aspect ratio. Comparing the settling parameter $\mathrm{Sv}$, the ratio of settling speed to wave speed, with the asymptotically small wave steepness $\epsilon$, we investigate the long time dynamics of a negatively buoyant particle. We examine the transition from aspect ratio-dependent equilibrium orientation in the weak settling regime ($\mathrm{Sv} \ll \epsilon^2$) to initial-condition-dependent alignment in the strong settling limit ($\mathrm{Sv} \gg 1$). Since translation and orientation are coupled for anisotropic particles, we use orientation dynamics to predict net horizontal transport. Fluid inertia induces an inertial torque that breaks the Stokesian degeneracy and drives broadside alignment. We analyze the influence of this torque on drift and alignment rate as functions of settling and wave parameters. Finally, we evaluate finite-size effects through the parameter $\sigma$, showing that a neutrally buoyant finite-size spheroid exhibits $\sigma$-dependent drift, validating the finite-size approximation when the spheroid size approaches the wavelength.