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Reflectionless wave propagation on shallow water with variable bathymetry and current

Published online by Cambridge University Press:  24 November 2021

Semyon M. Churilov Open the ORCID record for Semyon M. Churilov [Opens in a new window]  and
Yury A. Stepanyants Open the ORCID record for Yury A. Stepanyants [Opens in a new window]
Semyon M. Churilov
Affiliation:
Institute of Solar–Terrestrial Physics of the Siberian Branch of the Russian Academy of Sciences, P.O. Box 291, Irkutsk 664033, Russia
Yury A. Stepanyants*
Affiliation:
School of Sciences, University of Southern Queensland, West St., Toowoomba, QLD 4350, Australia Department of Applied Mathematics, Nizhny Novgorod State Technical University n.a. R.E. Alekseev, 24 Minin St., Nizhny Novgorod 603950, Russia
*
†Email address for correspondence: [email protected]
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Abstract

In the linear approximation, we study the one-dimensional problem of reflectionless wave propagation on the surface of a shallow duct with spatially varying water depth, duct width and current. We show that both global and bounded exact solutions describing the reflectionless propagation in opposite directions of long waves of arbitrary shape exist for the particular variations of these parameters. A general analysis of the problem is illustrated by a few solutions constructed for the specific cases of spatial profiles of the flow and wave propagation velocities. The results obtained can be of interest to mitigate the possible impact of waves on ships, marine engineering constructions and human activity in coastal zones.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Geophysical and Geological Flows: Ocean processes Geophysical and Geological Flows: Shallow water flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 931 , 25 January 2022 , A15
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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