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.

An investigation on the instability of a flexible liquid-filled rotor

“…Many related studies also focus on the problem of the fluid-structure interaction dynamics. 16–24 Ishida and Liu 25 applied a method, which utilizes discontinuous spring characteristics, to suppress unstable vibrations in an asymmetrical rotor system, an asymmetrical shaft system, and a rotor system partially filled with liquid. Nikiforov and Shokhin 26 presented the self-excitation of the rotor with radial walls and partially filled with liquid experimentally.…”