Roll Waves in Mudflow Modeled as Herschel–Bulkley Fluids
Publication: Journal of Engineering Mechanics
Volume 150, Issue 12
Abstract
We develop a multilayer model to study roll waves in mudflow of Herschel–Bulkley fluids initiated by periodic and localized disturbance. Simulations are conducted of the temporal development of periodic roll waves and spatial development of wave packets due to localized disturbance. The results of the temporal development are expressed in terms of the power-law index, the relative plug-layer thickness, the Froude number, and the perturbation wavelength. Our simulation for the spatial development shows the roll waves led by a dominant front runner and followed by a quiescent tail, closely reproducing a well-known river-clogging phenomenon of the natural mudflow observed in the mountain rivers on mild slopes. The leading wave of the roll-wave packet, i.e., the front runner, grows in depth, velocity, celerity, and wavelength with distance from the localized disturbance. The front-runner wave amplitude depends on the distance from the localized disturbance, the power law index, the plug-layer thickness, and the Froude number. We calculated the front-runner’s wave amplitude due to a line source of disturbance in a 1D unidirectional development and the roll waves’ 2D development due to a point source. The initial nonlinear growth in the 2D front runner is a fraction of the 1D waves, but the increase in the wave amplitude with distance follows the same trend. We have also conducted a mesh refinement study to determine the convergence and accuracy. The present simulations using 64 layers have attained an accuracy within a 2% error.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request. The source code used in this paper is available in a GitHub repository (Yu and Chu 2024).
Acknowledgments
Boyuan Yu and Vincent H. Chu acknowledge the valuable comments from anonymous reviewers. The authors would also like to thank the Basilisk and Gerris communities for useful insights and code sharing.
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Information
Published In
Journal of Engineering Mechanics
Volume 150 • Issue 12 • December 2024
Copyright
© 2024 American Society of Civil Engineers.
History
Received: Apr 5, 2024
Accepted: Jul 22, 2024
Published online: Sep 27, 2024
Published in print: Dec 1, 2024
Discussion open until: Feb 27, 2025
ASCE Technical Topics:
- Continuum mechanics
- Disaster risk management
- Disasters and hazards
- Dynamics (solid mechanics)
- Engineering mechanics
- Flow (fluid dynamics)
- Fluid dynamics
- Fluid mechanics
- Fluid velocity
- Froude number
- Geohazards
- Geology
- Geomorphology
- Geotechnical engineering
- Hydraulic engineering
- Hydrologic engineering
- Landslides
- Material mechanics
- Material properties
- Materials engineering
- Mountains
- Natural disasters
- River engineering
- Rivers and streams
- Solid mechanics
- Thickness
- Water and water resources
- Wave velocity
- Wavelength
- Waves (fluid mechanics)
- Waves (mechanics)
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