A particle model of rolling grain ripples under waves

Ken Haste Andersen

doi:10.1063/1.1332390

A particle model of rolling grain ripples under waves

Ken Haste Andersen

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Abstract

A simple model for the formation of rolling grain ripples on a flat sand bed by the oscillatory flow generated by a surface wave is presented. An equation of motion is derived for the individual ripples, seen as "particles," on the otherwise flat bed. The model accounts for the initial appearance of the ripples, the subsequent coarsening of the ripples, and the final equilibrium state. The model is related to the physical parameters of the problem, and an analytical approximation for the equilibrium spacing of the ripples is developed. It is found that the spacing between the ripples scales with the square-root of the nondimensional shear stress (the Shields parameter) on a flat bed. The results of the model are compared with measurements, and reasonable agreement between the model and the measurements is demonstrated. ©2001 American Institute of Physics.

Original language	English
Journal	Physics of Fluids
Volume	13
Issue number	1
Pages (from-to)	58-64
ISSN	1070-6631
DOIs	https://doi.org/10.1063/1.1332390
Publication status	Published - 2001

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Copyright (2001) American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics.

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N2 - A simple model for the formation of rolling grain ripples on a flat sand bed by the oscillatory flow generated by a surface wave is presented. An equation of motion is derived for the individual ripples, seen as "particles," on the otherwise flat bed. The model accounts for the initial appearance of the ripples, the subsequent coarsening of the ripples, and the final equilibrium state. The model is related to the physical parameters of the problem, and an analytical approximation for the equilibrium spacing of the ripples is developed. It is found that the spacing between the ripples scales with the square-root of the nondimensional shear stress (the Shields parameter) on a flat bed. The results of the model are compared with measurements, and reasonable agreement between the model and the measurements is demonstrated. ©2001 American Institute of Physics.

AB - A simple model for the formation of rolling grain ripples on a flat sand bed by the oscillatory flow generated by a surface wave is presented. An equation of motion is derived for the individual ripples, seen as "particles," on the otherwise flat bed. The model accounts for the initial appearance of the ripples, the subsequent coarsening of the ripples, and the final equilibrium state. The model is related to the physical parameters of the problem, and an analytical approximation for the equilibrium spacing of the ripples is developed. It is found that the spacing between the ripples scales with the square-root of the nondimensional shear stress (the Shields parameter) on a flat bed. The results of the model are compared with measurements, and reasonable agreement between the model and the measurements is demonstrated. ©2001 American Institute of Physics.

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DO - 10.1063/1.1332390

M3 - Journal article

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JO - Physics of Fluids

JF - Physics of Fluids

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A particle model of rolling grain ripples under waves

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