Roll waves as relaxation oscillations-Reference-Cited by-同舟云学术

Roll waves as relaxation oscillations

Published:2023-06-01 Issue:6 Volume:35 Page:
ISSN:1070-6631
Container-title:Physics of Fluids
language:en
Short-container-title:

Author:

Razis Dimitrios¹^ORCID,Kanellopoulos Giorgos²^ORCID,van der Weele Ko²^ORCID

Affiliation:

1. Department of Civil Engineering, University of Thessaly 1 , Volos 38334, Greece

2. Department of Mathematics, University of Patras 2 , Patras 26500, Greece

Abstract

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.

Publisher

AIP Publishing

Subject

Condensed Matter Physics,Fluid Flow and Transfer Processes,Mechanics of Materials,Computational Mechanics,Mechanical Engineering

Link

https://pubs.aip.org/aip/pof/article-pdf/doi/10.1063/5.0152549/18016144/063333_1_5.0152549.pdf

Reference39 articles.

1. The flow of water in an inclined channel of rectangular section;Philos. Mag.,1925

2. Mathematical solutions of the problem of roll waves in inclined open channels;Commun. Pure Appl. Math.,1949

3. Development of roll-wave trains in open channels;J. Hydraul. Div.,1969

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Pairwise balancing of forces in traveling granular waves;Physica D: Nonlinear Phenomena;2024-12

2. Undular bores in granular suspensions: a dynamical systems study;Nonlinear Dynamics;2024-07-23

3. Granular roll waves on a μ (J) rheology model: A dynamical systems perspective;Physics of Fluids;2024-02-01

4. Numerical study of roll wave development for non-uniform initial conditions using steep slope shallow water equations;Physics of Fluids;2024-02-01

5. Traveling Waves in Flowing Sand: The Dynamical Systems Approach;Chaos, Fractals and Complexity;2023