Pattern Formation inside a Rotating Cylinder Partially Filled with Liquid and Granular Medium

Abstract

The paper focuses on the experimental study of the dynamics of liquid and granular medium in a rapidly rotating horizontal cylinder. In the cavity frame gravity field performs rotation and produces oscillatory liquid flow, which is responsible for the series of novel effects; the problem corresponds to “vibrational mechanics”—generation of steady flows and patterns by oscillating force field. The paper presents the initial results of experimental study of a novel pattern formation effect which is observed at the interface between fluid and sand and which takes the form of ripples extended along the axis of rotation. The initial results of experimental research of a novel effect of pattern formation at the interface between fluid and sand in the form of ripples extended along the axis of rotation are presented. The spatial period of the patterns is studied in dependence on liquid volume, viscosity, and rotation rate. The experimental study of long time dynamics of pattern formation manifests that regular ripples transform into a series of dunes within a few minutes or dozens of minutes. The variety of patterns is determined by the interaction of two types of liquid flows induced by gravity: oscillatory and steady azimuthal flows near the sand surface.

Oscillatory and Steady Flows in the Annular Fluid Layer inside a Rotating Cylinder

“…Here, we present the initial experimental results on the velocity of the oscillatory fluid flow inside a rapidly rotating cylinder. We expect that the data obtained will facilitate the analysis of the phenomenon observed by Dyakova et al [4].…”

“…Additionally, for certain combinations of the rotation rate and the liquid volume, the excitation of the surface waves with various axial and azimuthal wavenumbers is possible [4,13]. The surface wave generates an oscillatory fluid flow, which has a frequency that is determined by the phase velocity of the wave.…”

“…This result gives the opportunity to determine the stability parameters of the centrifugal instability in the viscous boundary layer [5] and the onset of a quasistationary relief at the interface between the granular medium and the fluid inside a rotating cylinder [4]. The specific feature of these problems is the inability to experimentally measure the velocity of the oscillatory fluid motion near the Stokes boundary layer.…”

“…The oscillatory motion of the annular layer is of great interest for both fundamental hydrodynamic research and astrophysical applications. Dyakova et al [4] experimentally determined that the oscillatory fluid flow above the granular medium inside a rotating cylinder causes the onset of the instability at the fluid-granular medium interface and that the subsequent onset of a quasistationary relief in the form of ripples extended along the axis of rotation. The stability parameter requires determination of the velocity of the fluid oscillations near the interface.…”