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Pattern formation in a vibrated granular layer: the pattern selection issue

Clement¹, Labous

¹Laboratoire des Milieux Desordonnes et Heterogenes, CNRS UMR No. 7603, Universite Pierre et Marie Curie, Boite Postale 86, 4 Place Jussieu, F-75252 Paris, France.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

|January 4, 2001

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This study numerically investigates surface instabilities in vibrated granular layers, identifying two distinct wavelength selection regimes. Findings reveal frequency-dependent and height-dependent patterns, offering insights into granular dynamics.

Area of Science:

Physics
Granular Mechanics
Fluid Dynamics

Background:

Surface instabilities in granular materials are complex phenomena.
Understanding pattern formation in vibrated granular layers is crucial for various applications.

Purpose of the Study:

To numerically investigate surface instabilities in a bidimensional vibrated granular layer.
To identify and characterize the mechanisms driving stationary wave formation and wavelength selection.

Main Methods:

Numerical simulation of a bidimensional vibrated granular layer.
Analysis of surface instability and stationary wave formation.
Dimensional analysis for empirical relation development.

Main Results:

Related Experiment Videos

Two distinct wavelength selection regimes were identified: dispersive and saturation.
In the dispersive regime, wavelength decreases with increasing frequency.
In the saturation regime, wavelength is constant and depends on layer height, linked to dissipative gas instabilities.

Conclusions:

An empirical relation for the dispersive regime was proposed based on dimensional arguments.
The saturation regime's pattern formation is connected to intrinsic instabilities in dissipative gases.
Layer height dependence is explained by grain collision dissipation mechanisms.