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Surface water waves over a shallow canopy

Published online by Cambridge University Press:  11 March 2015

Benlong Wang ,
Xiaoyu Guo  and
Chiang C. Mei
Benlong Wang
Affiliation:
Ministry of Education Key Laboratory of Hydrodynamics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 200240 Shanghai, China
Xiaoyu Guo
Affiliation:
Ministry of Education Key Laboratory of Hydrodynamics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 200240 Shanghai, China
Chiang C. Mei*
Affiliation:
Ministry of Education Key Laboratory of Hydrodynamics, School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, 200240 Shanghai, China Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
*
†Email address for correspondence: ccmei@mit.edu
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Abstract

The dynamics of water waves passing over a vegetation canopy is modelled theoretically. To simplify the geometry, we examine a periodic array of vertical cylinders fixed on a slowly varying seabed. The macroscale behaviour of wave attenuation is predicted based on microscale dynamics between plants. Interstitial turbulence is modelled by Reynolds equations with a locally constant eddy viscosity determined by energy considerations. Using the asymptotic method of multiple-scale expansions, the slow evolution of waves is derived by considering the coupling with the small-scale motion in the canopy. After numerical solution of the canonical boundary-value problem in a few unit cells, predictions of macroscale effects such as wave attenuation are made and compared with laboratory experiments. The counteracting effects of shoaling and dissipation are discussed for different vegetation densities.

JFM classification

Geophysical and Geological Flows: Coastal engineering Waves/Free-surface Flows: Surface gravity waves

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Papers
Information
Journal of Fluid Mechanics , Volume 768 , 10 April 2015 , pp. 572 - 599
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© 2015 Cambridge University Press 

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