Waves of intermediate length through an array of vertical cylinders
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10652_2013_Article_9308.pdf
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1.3 MB
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Checksum (MD5)
966e1e9624c16f56a9a005d6a327756a
Author(s)
Chan, I. -Chi
Liu, Philip L. -F.
Mei, Chiang Chung
Date Issued
September 2013
Journal
Environmental Fluid Mechanics
Publisher
Springer Netherlands
Citation
Mei, Chiang C., I. -Chi Chan, and Philip L. -F. Liu. “Waves of Intermediate Length through an Array of Vertical Cylinders.” Environmental Fluid Mechanics 14.1 (2014): 235–261.
Version
Author's final manuscript
Abstract
We report a semi-analytical theory of wave propagation through a vegetated water. Our aim is to construct a mathematical model for waves propagating through a lattice-like array of vertical cylinders, where the macro-scale variation of waves is derived from the dynamics in the micro-scale cells. Assuming infinitesimal waves, periodic lattice configuration, and strong contrast between the lattice spacing and the typical wavelength, the perturbation theory of homogenization (multiple scales) is used to derive the effective equations governing the macro-scale wave dynamics. The constitutive coefficients are computed from the solution of micro-scale boundary-value problem for a finite number of unit cells. Eddy viscosity in a unit cell is determined by balancing the time-averaged rate of dissipation and the rate of work done by wave force on the forest at a finite number of macro stations. While the spirit is similar to RANS scheme, less computational effort is needed. Using one fitting parameter, the theory is used to simulate three existing experiments with encouraging results. Limitations of the present theory are also pointed out.
MIT Department
Massachusetts Institute of Technology. Department of Civil and Environmental Engineering
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Creative Commons Attribution-NonCommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/s10652-013-9308-1
