The Geometry of Sand Ripples in a Uniformly Rotating and Librating Horizontal Cylinder
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ORIGINAL ARTICLE
The Geometry of Sand Ripples in a Uniformly Rotating and Librating Horizontal Cylinder Denis Polezhaev 1 Received: 17 March 2020 / Accepted: 7 June 2020 # Springer Nature B.V. 2020
Abstract Regular ripples at the interface between the granular medium and the fluid in a rapidly rotating cylinder are experimentally studied. We consider two types of ripple formation. First, the ripple formation in a uniformly rotating horizontal cylinder filled with granular medium, fluid and air. In this case, oscillations of the multiphase system in the rotating reference frame are excited by gravity. Second, the ripple formation under the fluid oscillations in a cylinder filled with fluid and granular medium and rotating with a modulated rotation rate (librating cylinder). For this type of ripple formation, the effect of gravity is negligible compared to that of centrifugal force of inertia. It is found that the ripple azimuthal length is determined by the angular amplitude of the fluid oscillations in the vicinity of the sand bed and is not affected by the frequency of the fluid oscillations. The experimental data on the steepness of both types of the ripples favorably agree with each other and predictions of (Nielsen in J. Geophys. Res. Oceans 86(C7): 6467-6472, 1981). Differences in experimental research between normal gravity and microgravity are highlighted. Keywords Ripples . Fluid . Granular medium . Rotation . Oscillations
Introduction In the nearshore zone, the gravity wave propagation over a sandy bed can cause the appearance of small scale sedimentary structures. Such bed forms, known as ripples, have a significant influence on the structure of the boundary layer as well as on the sediment transport mechanism. Sea ripples have been studied intensively both theoretically and experimentally under field and controlled conditions. The geometric characteristics of ripples (wavelength and height) depend on near-bed amplitude and frequency of oscillations, fluid density and viscosity, and sediment density and size. These values are combined in various ways in order to deduce a series of nondimensional parameters used in sediment dynamics such as the mobility number, Shields number, the ratio of the amplitude of fluid oscillations to the grain size, etc. Typically, ripples are divided into three groups: orbital, anorbital and suborbital, depending on flow and particle characteristics * Denis Polezhaev [email protected] 1
Laboratory of Vibrational Hydromechanics, Perm State Humanitarian Pedagogical University, Perm, Russia
(Wiberg and Harris 1994). Orbital ripples are relatively steep ripples whose wavelength tends to scale with amplitude of fluid oscillations. Anorbital ripples arise when the ratio of the amplitude to the grain diameter exceeds approximately 2 × 103, and the ripple wavelength becomes dependent only on the particle size. Suborbital ripples are intermediate forms between these two primary ripple types with wavelengths and steepness smaller than those of orbital ripples, and larger than those
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