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

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 $ω$ 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 $h$, $ω$ 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 $hωr$. 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.