Oscillation-induced sand dunes in a liquid-filled rotating cylinder.

Abstract

The dynamics of granular medium in a liquid-filled horizontal cylinder with a time-varying rotation rate is experimentally studied. When the cylinder is purely rotated, the granular medium develops an annular layer near the cylindrical wall. The interface between fluid and sand is smooth and axisymmetric. The time variation of the rotation rate initiates the azimuthal oscillation of the liquid in the cylinder's frame of reference and provokes the onset of quasisteady relief in the form of regular dunes. The stability of the axisymmetric sand surface and dynamics of regular dunes are examined. It is found that the ripple formation is provoked by the quasisteady instability of the Stokes boundary layer. In the range of high Reynolds numbers, the ripple formation occurs at a constant critical Shields number θ_{c}≃0.05. The spatial period of the relief is not sensitive to the fluid viscosity and granule diameter; it is determined by the amplitude of oscillation and ratio between the oscillation frequency and mean rotation rate. Long-term experiments show that there are forward and backward azimuthal drifts of dunes. An initial analysis of the issues related to the dune migration is provided.