Granular spirals on erodible sand bed submitted to a circular fluid motion

TL;DR

This study experimentally investigates spiral ripple patterns formed on a granular sand bed under circular fluid motion, revealing how pattern characteristics depend on flow speed, water height, and radial position, and linking pattern formation to fluid momentum.

Contribution

It provides a detailed phase diagram and quantitative analysis of spiral pattern formation, highlighting the dependence on fluid flow parameters and challenging boundary layer instability explanations.

Findings

Ripple wavelength decreases with increasing rotation speed.

Spiral arm angle scales with water height, rotation speed, and radius.

Critical radius for pattern onset depends on flow parameters.

Abstract

An experimental study of a granular surface submitted to a circular fluid motion is presented. The appearance of an instability along the sand-water interface is observed beyond a critical radius $r_c$. This creates ripples with a spiral shape on the granular surface. A phase diagram of such patterns is constructed and discussed as a function of the rotation speed $\omega$ of the flow and as a function of the height of water $h$ above the surface. The study of $r_c$ as a function of $h$, $\omega$ and $r$ parameters is reported. Thereafter, $r_c$ is shown to depend on the rotation speed according to a power law. The ripple wavelength is found to decrease when the rotation speed increases and is proportional to the radial distance $r$. The azimuthal angle \az of the spiral arms is studied. It is found that \az scales with $h\omega r$. This lead to the conclusion that \az depends on the fluid momentum. Comparison with experiments performed with fluids allows us to state that the spiral patterns are not the signature of an instability of the boundary layer.