TY - JOUR

T1 - Waves of intermediate length through an array of vertical cylinders

AU - Mei, Chiang C.

AU - Chan, I. Chi

AU - Liu, Philip L.F.

N1 - Funding Information:
Acknowledgments This work is supported by research grants from the National Science Foundation to Cornell University. CCM was also funded by a Mary Upson visiting professorship from Cornell University.

PY - 2014/2

Y1 - 2014/2

N2 - 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.

AB - 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.

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U2 - 10.1007/s10652-013-9308-1

DO - 10.1007/s10652-013-9308-1

M3 - Article

AN - SCOPUS:84892449479

SN - 1567-7419

VL - 14

SP - 235

EP - 261

JO - Environmental Fluid Mechanics

JF - Environmental Fluid Mechanics

IS - 1

ER -