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Generating the granular solitary wave

Published online by Cambridge University Press:  20 November 2025

Giorgos Kanellopoulos Open the ORCID record for Giorgos Kanellopoulos [Opens in a new window] ,
Dimitrios Razis Open the ORCID record for Dimitrios Razis [Opens in a new window]  and
Ko van der Weele Open the ORCID record for Ko van der Weele [Opens in a new window]
Giorgos Kanellopoulos
Affiliation:
Department of Mathematics, University of Patras, 26500 Patras, Greece
Dimitrios Razis
Affiliation:
Department of Mathematics, University of Patras, 26500 Patras, Greece Mathematics Research Center, Academy of Athens, 11527 Athens, Greece Department of Physics, National & Kapodistrian University of Athens, 15771 Ilisia Athens, Greece
Ko van der Weele*
Affiliation:
Department of Mathematics, University of Patras, 26500 Patras, Greece
*
Corresponding author: Ko van der Weele, weele@math.upatras.gr
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Abstract

Based on the generalised Saint-Venant equations for granular flow on an inclined chute, we show how to generate solitary waves from localised perturbations at the inlet. Such perturbations usually give rise to a group of roll waves, but by choosing the system parameters appropriately, the formation of all but the first wave can be suppressed, thus turning this first one into a solitary wave. This calls for a highly diffusive flow, which is realised for inclination angles close to the minimal angle required to keep the granular material flowing.

JFM classification

Waves/Free-surface Flows: Channel flow Granular media: Dry granular material Waves/Free-surface Flows: Solitary waves

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 1023 , 25 November 2025 , A27
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Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Supplementary material: File

Kanellopoulos et al. supplementary movie

Video showing the generation and evolution of a granular solitary wave on a 50 m chute. The formation of the wave is triggered by an initial condition mimicking localized random perturbations at the inlet of the chute. During the early stages (up to t = 5 s), the humps of the initial perturbation are seen to merge. Simultaneously, they sweep up material from the carrying flow, as evidenced by the formation of a valley in the wake of the travelling compound. After t = 5 s, a solitary wave emerges, featuring a steep wave front and a relatively long tail followed by a gradually deepening valley. This waveform keeps growing slowly until it exits the chute. The suppression of any secondary waves is due to the strong diffusion in the flowing sheet (controlled via the tilting angle, which is just slightly above the angle of repose), while the slow growth of the solitary wave is a result of the fact that the carrying flow is sufficiently energetic (controlled via the Froude number of the incoming flow). The system parameters in this video are the same as those of Fig. 5 in the main text.
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