Erosion by the unsteady motion of a disk close to a granular bed

Flatfish, such as flounders, bury themselves in the sand to hide from predators. They are able to hide very quickly : with a few oscillations of their fins close to the seabed, they suspend sand, which then falls onto their body. This study aims at better understanding this natural behaviour by simplifying it in the laboratory. To do so, a rigid disk of diameter D replicates the behaviour of the flatfish : the disk can oscillate at a frequency f and an amplitude L/2 at a minimum distance h₀ from a flat granular bed.

We focus here on a half-oscillation, which means that the disk only moves downwards or upwards once with smooth acceleration and deceleration. The disk travels the distance L in a characteristic time τ. The motion of the disk is responsible for the formation of a vortex ring due to the roll-up of the shear layer produced at the edge of the disk. The influence of L, D and h₀ as well as the initial position of the disk, on the flow is experimentally investigated by Particle Image Velocimetry (PIV) and numerically with the open-source code Basilisk. The axisymmetric numerical simulations are in good agreement with the experimental results. The time evolution of the vortex-ring circulation Γ, radius a and location relative to the disk

is determined, as well as scaling laws in relation to the parameters of the disk motion.

The characterization of the flow field helps to understand the erosion of the granular bed. It highlights the competitive effects on the erosion of the interaction of the vortex ring with the granular bed and the fluid ejection/injection between the disk and the granular bed.