Surface water waves over a shallow canopy

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Abstract

<jats:p>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.</jats:p>

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