Numerical Modeling of Surface Waves over Submerged Flexible Vegetation
Publication: Journal of Engineering Mechanics
Volume 141, Issue 8
Abstract
This paper presents a coupled wave–vegetation model for simulating the interaction between water waves and submerged flexible plants. The balance of forces for the vegetation motion includes buoyancy, damping, stiffness of the vegetation, and gravity as restoring forces, and drag and inertia as driving forces. The governing equation for vegetation motion is solved by the high-order finite element method (FEM) together with an implicit time differencing scheme. The results of the vegetation model exhibit a fourth-order convergence rate. The vegetation-induced drag and inertia are introduced into the wave model as a source term in the momentum equation. This coupled model is rigorously verified by comparing numerical results with theoretical solutions for single swaying vegetation cases and with experimental data for large-scale swaying vegetation cases. Excellent agreement is achieved. A scaling analysis is performed on the governing equation for vegetation motion to understand the importance of each force involved in the vegetation vibration. For cases in which damping becomes significant compared with other restoring forces, a theoretical relationship between movements of vegetation stem and water particle is derived, and a dimensionless parameter, incorporating characteristics of waves and material as well as geometric properties of vegetation, is obtained. The vegetation deformation model developed in this paper can be coupled with other wave models to simulate wave and vegetation interactions.
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Acknowledgments
The study was supported by the U.S. National Science Foundation (NSF) (CBET-0652859 and DMS-1115527). Dr. Yavuz Ozeren provided us with his laboratory data for model verification. Suggestions and comments on the high-order FEM by Drs. Don Liu and Xiaoliang Wan were helpful. Comments from two anonymous reviewers improved the manuscript. Any opinions, findings and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reflect the views of the NSF.
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Published In
Journal of Engineering Mechanics
Volume 141 • Issue 8 • August 2015
Copyright
© 2015 American Society of Civil Engineers.
History
Received: Mar 16, 2014
Accepted: Dec 5, 2014
Published online: Apr 24, 2015
Published in print: Aug 1, 2015
Discussion open until: Sep 24, 2015
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