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

Clint Wong, Aggelos Dimakopoulos, Philippe Trinh, Jonathan Chapman

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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).
Original languageEnglish
Article numberA3
JournalJournal of Fluid Mechanics
Issue numberA3
Early online date25 Jan 2022
Publication statusPublished - 25 Mar 2022

Bibliographical note

Funding Information:
This publication is based on work partially supported by the EPSRC Centre for Doctoral Training in Industrially Focused Mathematical Modelling (EP/L015803/1) in collaboration with HR Wallingford and US Army Engineer Research and Development Center (ERDC). We would like to thank C. Kees and T. de Lataillade from US Army ERDC for their important contributions. We are also grateful to I. Hewitt (Oxford) and P. Milewski (Bath) for their helpful suggestions.


  • coastal engineering
  • surface gravity waves
  • wave-structure interactions

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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