TY - JOUR
T1 - Periodic water waves through suspended canopy
AU - Hu, Jie
AU - Tang, Xiaochun
AU - Lin, Pengzhi
AU - Liu, Philip L.F.
N1 - Funding Information:
This work was partially supported by National University of Singapore (NUS). P. L.-F. Liu would also like to acknowledge the support from National Research Foundation, Prime Minister’s Office, Singapore under its Marine Science Research and Development Program (Award No. MSRDP-05 ). J Hu has been supported by a PhD Research Scholarship at NUS thanks to the Ministry of Education in Singapore.
Publisher Copyright:
© 2020 Elsevier B.V.
PY - 2021/1
Y1 - 2021/1
N2 - Small-amplitude water waves passing through a suspended canopy is studied. The area of suspended canopy is modeled by an array of vertical rigid cylinders with periodic spacing. Assuming that the diameter of cylinders and their spacing are much smaller than the typical incident wavelength, the homogenization theory (method of multiple-scale perturbation) is applied to create coupled micro-scale (cylinder spacing) and macro-scale (wavelength) problems. The micro-scale problem describes turbulent flows within a unit cell of the cylinder array, being driven by the macro-scale pressure gradients. Employing the concept of averaged energy balance over a wave period, the micro-scale flows determine the eddy viscosity, which damps the waves in the macro-scale flows. Eigenfunction expansions method is used to solve the macro-scale problem, in which a complex frequency dispersion relation is solved numerically by a multiple successive approximation technique. The potential decomposition method, which can avoid solving a complex frequency dispersion relation, is also employed to validate the accuracy of the eigenfunction expansions method. Both methods yield accurate solutions. However, the eigenfunction expansions method is relatively straightforward and can unify the solutions for suspended canopy and emergent vegetation. A new set of flume experiments of waves through suspended canopy is conducted and experimental data are used to check present solutions. Very good agreement has been observed. Finally, the effectiveness of suspended canopy, submerged and emergent vegetation on wave attenuation is discussed.
AB - Small-amplitude water waves passing through a suspended canopy is studied. The area of suspended canopy is modeled by an array of vertical rigid cylinders with periodic spacing. Assuming that the diameter of cylinders and their spacing are much smaller than the typical incident wavelength, the homogenization theory (method of multiple-scale perturbation) is applied to create coupled micro-scale (cylinder spacing) and macro-scale (wavelength) problems. The micro-scale problem describes turbulent flows within a unit cell of the cylinder array, being driven by the macro-scale pressure gradients. Employing the concept of averaged energy balance over a wave period, the micro-scale flows determine the eddy viscosity, which damps the waves in the macro-scale flows. Eigenfunction expansions method is used to solve the macro-scale problem, in which a complex frequency dispersion relation is solved numerically by a multiple successive approximation technique. The potential decomposition method, which can avoid solving a complex frequency dispersion relation, is also employed to validate the accuracy of the eigenfunction expansions method. Both methods yield accurate solutions. However, the eigenfunction expansions method is relatively straightforward and can unify the solutions for suspended canopy and emergent vegetation. A new set of flume experiments of waves through suspended canopy is conducted and experimental data are used to check present solutions. Very good agreement has been observed. Finally, the effectiveness of suspended canopy, submerged and emergent vegetation on wave attenuation is discussed.
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U2 - 10.1016/j.coastaleng.2020.103809
DO - 10.1016/j.coastaleng.2020.103809
M3 - Article
AN - SCOPUS:85096222230
SN - 0378-3839
VL - 163
JO - Coastal Engineering
JF - Coastal Engineering
M1 - 103809
ER -