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The front runner in roll waves produced by local disturbances

Published online by Cambridge University Press:  14 December 2021

Boyuan Yu  and
Vincent H. Chu Open the ORCID record for Vincent H. Chu [Opens in a new window]
Boyuan Yu
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, QC, H3A 0C3, Canada
Vincent H. Chu*
Affiliation:
Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, QC, H3A 0C3, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Roll waves produced by a local disturbance comprise a group of shock waves with steep fronts. We used a robust and accurate numerical scheme to capture the steep fronts in a shallow-water hydraulic model of the waves. Our simulations of the waves in clear water revealed the existence of a front runner with an exceedingly large amplitude – much greater than those of all other shock waves in the wave group. The trailing waves at the back remained periodic. Waves were produced continuously within the group due to nonlinear instability. The celerity depended on the wave amplitude. Over time, the instability produced an increasing number of shock waves in an ever-expanding wave group. We conducted simulations for three types of local disturbances of very different duration over a range of amplitudes. We interpreted the simulation results for the front runner and the trailing waves, guided by an analytical solution and the laboratory data available for the smaller waves in the trailing end of the wave group.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Geophysical and Geological Flows: River dynamics Waves/Free-surface Flows: Channel flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 932 , 10 February 2022 , A42
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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