Surface water waves over a shallow canopy

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.

Current blockage and extreme forces on a jacket model in focussed wave groups with current

“…The overall Morison inertia coefficient, C m , is set as 2.0, which is the potential flow-based value for cylinders in cross flow. It is worth noting that some early studies for periodic waves and current separately have demonstrated that C d can be larger for cylinder array than an isolated cylinder, see Cheng and Nguyen (2010); Wang et al (2015).…”

Multiscale evaluation method of the drag effect on shallow water flow through coastal forests based on 3D numerical simulations

“…In particular, examining the 2D velocity profiles in detail in Section 4, we find that the flow velocities in the cases with relatively high depths (Cases 6 and 7) are There is also a limitation such that the current framework could only deal with the stable, quasi-steady and macroscopically unidirectional flow situation. We formulate SW equation (27) without inertial force effects like many previous studies. 45 However, the inertial force is dominant in dense forests under unsteady-state flow conditions especially at the tsunami runup.…”

“…In some previous studies with purposes similar to ours, the length of the LTD in the overall flow direction was reduced to accommodate only a few trees. For example, Wang et al 27 employed a periodic LTD, called a unit cell, in which cylinders are vertically located to develop a surface water model. Lee and Yang 31 also investigated flows in a 2D unit cell with emerged cylinders.…”

“…In this type of modeling, the macroscopic damping effect of trees on the global flow is associated with the cell-averaged values of the local flow characteristics. [26][27][28] As emphasized in Liu et al, 28 numerical analyses based on multiscale modeling have a computational efficiency advantage over 3D simulations, and they provide deeper physical insights than macroscopic empirical approaches. Based on the principles of this approach, predictions of global flow through coastal forests can be efficiently conducted without ignoring the local flow characteristics around individual trees.…”

Comprendre le rôle des récifs barrière à Posidonia oceanica dans l’atténuation de l’hydrodynamique : Programme CANOPé

“…La capacité à atténuer les forçages hydrodynamiques est dépendante des caractéristiques biométriques comme la densité (PAUL & AMOS, 2011 ;KOFTIS et al, 2013), l'indice de surface foliaire (PAUL et al, 2012), la flexibilité (PERALTA et al, 2008 ;PUJOL & NEPF, 2012), le ratio de submersion (MANCA et al, 2012 ;JOHN et al, 2016), et des caractéristiques morphologiques (étendue -GAMBI et al, 1990, fragmentation -FONSECA & KOEHL, 2006 de chaque espèce (ELGINOZ et al, 2011). À notre connaissance, seules deux études récentes se sont intéressées au rôle de la végétation en très faible profondeur (WANG et al, 2015) dernières produisant les vents les plus intenses (figure 1b). Trois sites ateliers ont été choisis pour leurs différentes expositions aux forçages hydrodynamiques et leur variété de longueur de fetch (figure 1a).…”