Experimental investigation of inertial spheres settling in surface gravity waves

We investigate the motion of weakly negatively buoyant spheres settling in surface gravity waves using laboratory experiments. The trajectories of the settling spheres are tracked over most of the water depth with simultaneous measurements of the background fluid flow. These experiments are conducted in the regime relevant for environmental and geophysical applications where both particle inertia and fluid inertia are important. Using these data, we show that the sphere motion is well described by the kinematic sum of the undisturbed fluid velocity and the particle terminal settling velocity as long as the fluid inertia is not too large. We show how this result can be understood in the context of an ad hoc Maxey–Riley–Gatignol-type equation where the drag on the particle is given by the Schiller–Naumann drag correlation. We also evaluate whether inertial particles experience enhanced settling in waves, finding that measurement uncertainties in the particle terminal settling velocity and the presence of Eulerian-mean flows do not allow the small percentage increase in the settling velocity to be measured. When the fluid inertia becomes large enough, we observe path instabilities caused by particle wake effects in both quiescent and wavy conditions. However, the particle velocity fluctuations associated with the path instabilities are unaffected by the background flow. The minimal influence of the wavy flow on the particle path instabilities is thought to be due to the large-scale separation between the waves and the particle.