Roll waves as relaxation oscillations

Granular roll waves consist of a long rising flank, followed by an abrupt fall. Based on this observation, we draw a parallel between roll waves and relaxation oscillations. From the generalized Saint-Venant equations, we derive a dynamical system governing the shape of the waves. Casting this syste...

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Bibliographic Details
Published in:Physics of fluids (1994) 2023-06, Vol.35 (6)
Main Authors: Razis, Dimitrios, Kanellopoulos, Giorgos, van der Weele, Ko
Format: Article
Language:English
Subjects:
Dynamical systems
Fluid dynamics
Physics
Relaxation oscillations
Water waves
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Summary:Granular roll waves consist of a long rising flank, followed by an abrupt fall. Based on this observation, we draw a parallel between roll waves and relaxation oscillations. From the generalized Saint-Venant equations, we derive a dynamical system governing the shape of the waves. Casting this system in the Liénard form, custom-made for studying relaxation oscillations, we find an analytical expression for the wavelength of roll waves as a function of their amplitude.
ISSN:1070-6631
1089-7666
DOI:10.1063/5.0152549