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Multiple-scales analysis of wave evolution in the presence of rigid vegetation

Published online by Cambridge University Press:  25 January 2022

Clint Y.H. Wong Open the ORCID record for Clint Y.H. Wong [Opens in a new window] ,
Aggelos S. Dimakopoulos ,
Philippe H. Trinh Open the ORCID record for Philippe H. Trinh [Opens in a new window]  and
S. Jonathan Chapman Open the ORCID record for S. Jonathan Chapman [Opens in a new window]
Clint Y.H. Wong*
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OxfordOX2 6GG, UK
Aggelos S. Dimakopoulos
Affiliation:
HR Wallingford, Howbery Park, WallingfordOX10 8BA, UK
Philippe H. Trinh
Affiliation:
Department of Mathematical Sciences, University of Bath, BathBA2 7AY, UK
S. Jonathan Chapman
Affiliation:
Oxford Centre for Industrial and Applied Mathematics, Mathematical Institute, University of Oxford, OxfordOX2 6GG, UK
*
†Email address for correspondence: clintwong@cantab.net
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Abstract

The study of free-surface flows over vegetative structures presents a challenging setting for theoretical, computational and experimental analysis. In this work, we develop a multiple-scales asymptotic framework for the evolution of free-surface waves over rigid vegetation and a slowly varying substrate. The analysis quantifies the balance between the competing effects of vegetation and shoaling, and provides a prediction of the amplitude as the wave approaches a coastline. Our analysis unifies and extends existing theories that study these effects individually. The asymptotic predictions are shown to provide good agreement with full numerical simulations (varying depth) and published experimental results (constant depth).

JFM classification

Waves/Free-surface Flows: Wave-structure interactions Waves/Free-surface Flows: Surface gravity waves Geophysical and Geological Flows: Coastal engineering
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 935 , 25 March 2022 , A3
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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