Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-28T21:38:09.908Z Has data issue: false hasContentIssue false
  • English
  • Français

Long waves through emergent coastal vegetation

Published online by Cambridge University Press:  14 October 2011

Chiang C. Mei ,
I-Chi Chan ,
Philip L.-F. Liu ,
Zhenhua Huang  and
Wenbin Zhang
Chiang C. Mei*
Affiliation:
Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
I-Chi Chan
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
Philip L.-F. Liu
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA Institute of Hydrological and Oceanic Sciences, National Central University, Jhongli, Taiwan, 32001
Zhenhua Huang
Affiliation:
Earth Observatory of Singapore and Department of Civil and Environmental Engineering, Nanyang Technological University, Singapore 639398
Wenbin Zhang
Affiliation:
Earth Observatory of Singapore and Department of Civil and Environmental Engineering, Nanyang Technological University, Singapore 639398
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the effects of emergent coastal forests on the propagation of long surface waves of small amplitude. The forest is idealized by an array of vertical cylinders. Simple models are employed to represent bed friction and to simulate turbulence generated by flow through the tree trunks. A multi-scale (homogenization) analysis similar to that for seepage flows is carried out to deduce the effective equations on the macro-scale. The effective coefficients are calculated by numerically solving the micro-scale problem in a unit cell surrounding one or several cylinders. Analytical and numerical solutions for wave attenuation on the macro-scale for different bathymetries and coastal forest configurations are presented. For a transient incident wave, analytical results are discussed for the damping of a leading tsunami. For comparison series of laboratory data for periodic and transient incident waves are also presented. Good agreement is found even though some of the measured waves are short or nonlinear.

JFM classification

Geophysical and Geological Flows: Shallow water flows Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 687 , 25 November 2011 , pp. 461 - 491
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Augustin, L. N., Irish, J. L. & Lynett, P. 2009 Laboratory and numerical studies of wave damping by emergent and near-emergent wetland vegetation. Coast. Engng 56, 332–340.CrossRefGoogle Scholar
2. Auriault, J.-L. 1980 Dynamic behavior of a porous medium saturated by a Newtonian fluid. Internat. J. Eng. Sci. 18, 775–785.CrossRefGoogle Scholar
3. Bateman, H. 1954 Table of Integral Transforms, vol. 1 (ed. Erdrélyi, A. ). McGraw-Hill.Google Scholar
4. Carmen, P. C. 1937 Fluid flow through granular beds. Trans. Inst. Chem. Engrs 15, 15–16.Google Scholar
5. Carslaw, H. S. & Jaeger, J. C. 1963 Operational Methods in Applied Mathematics. Dover.Google Scholar
6. Danielsen, F., Sørensen, M. K., Olwig, M. F., Selvam, V., Parish, F. & Burgess, N. D. 2005 The asian tsunami: a protective role for coastal vegetation. Science 310, 643.CrossRefGoogle Scholar
7. Dasa, S. & Vincent, J. R. 2009 Mangroves protected villages and reduced death toll during Indian super cyclone. Proc. Natl Acad. Sci. USA 106, 7357–7360.CrossRefGoogle Scholar
8. Ene, H. L. & Sanchez-Palencia, E. 1975 Équations et phénomènes de surface pour l’écoulement dans un modèle de milieu poreux. J. Méc. 14, 73–108.Google Scholar
9. Fernando, H. J. S., Samarawickrama, S. P., Balasubramanian, S., Hettiarachchi, S. S. L. & Voropayev, S. 2008 Effects of porous barriers such as coral reefs on coastal wave propagation. J. Hydro-environ. Res. 1, 187–194.CrossRefGoogle Scholar
10. Hiraishi, T. & Harada, K. 2003 Greenbelt tsunami prevention in south-Pacific region. Rep. Port and Airport Research Institute 43 (2), 1–23.Google Scholar
11. Huang, Z., Yao, Yao, Sim, S. Y. & Yao, Yu 2010 Interaction of solitary waves with emergent rigid vegetation. Ocean Engng 38, 1080–1088.CrossRefGoogle Scholar
12. Irtem, E., Gedik, N., Kabdasli, M. S. & Yasa, N. E. 2009 Coastal forest effects on tsunami run-up heights. Ocean Engng 36, 313–320.CrossRefGoogle Scholar
13. Kajiura, K. 1963 The leading wave of a tsunami. Bull. Earthq. Res. 41, 525–571.Google Scholar
14. Keller, J. B. 1980 Darcy’s law for flow in porous media and the two-space method. In Nonlinear Partial Differential Equations in Engineering and Applied Science (ed. Sternberg, R. L. et al. ). Lecture Notes in Pure and Applied Mathematics , vol. 54. pp. 429–443. Dekker.Google Scholar
15. Keller, J. B. & Keller, H. B. 1964 Water wave run-up on a beach. ONR. Res. Rep. Contract No. NONNR-3828(00), Department of the Navy.CrossRefGoogle Scholar
16. Kobayashi, N., Raichlen, A. W. & Asano, T. 1993 Wave attenuation by vegetation. J. Waterways Port Coast. Ocean Engng 119, 30–48.CrossRefGoogle Scholar
17. Liu, P. L.-F., Lynett, P., Fernando, H., Jaffe, B. E., Fritz, H., Higman, B., Morton, R., Goff, J. & Synolakis, C. 2005 Observations by the international tsunami survey team in Sri Lanka. Science 308, 1595.CrossRefGoogle ScholarPubMed
18. Mazda, Y., Kobashi, D. & Okada, S. 2005 Tidal-scale hydrodynamics within mangrove swamps. Wetlands Ecol. Manage. 13, 647–655.CrossRefGoogle Scholar
19. Massel, S. R., Furukawa, K. & Binkman, R. M. 1999 Surface wave propagation in mangrove forests. Fluid Dyn. Res. 24, 219–249.CrossRefGoogle Scholar
20. Mei, C. C. 1983 The Applied Dynamics of Ocean Surface Waves. Wiley.Google Scholar
21. Mei, C. C. & Vernescu, B. 2010 Homogenization Methods for Multiscale Mechanics. World Scientific.CrossRefGoogle Scholar
22. Möller, I. 2006 Quantifying saltmarsh vegetation and its effect on wave height dissipation: results from a UK East coast saltmarsh. Estuar. Coast. Shelf Sci. 69, 337–351.CrossRefGoogle Scholar
23. Möller, I., Spencer, T., French, J. R., Leggett, D. J. & Dixon, M. 1999 Wave transformation over salt marshes: a field and numerical modelling study from North Norfolk, England. Estuar. Coast. Shelf Sci. 49, 411–426.CrossRefGoogle Scholar
24. Nepf, H. M. 1999 Drag, turbulence, and diffusion in flow through emergent vegetation. Water Resour. Res. 35, 479–489.CrossRefGoogle Scholar
25. Nielsen, P. 1992 Coastal Bottom Boundary Layers and Sediment Transport. World Scientific.CrossRefGoogle Scholar
26. Phillips, O. M. 1977 Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
27. Sheng, P. & Zhou, M. Y. 1988 Dynamic permeability of porous media. Phy. Rev. Lett. 61, 1951–1954.CrossRefGoogle ScholarPubMed
28. Suzuki, T., Dijkstra, J. & Stive, M. J. F. 2008 Wave dissipation on a vegetated salt marsh. Proc. Intl Conf. Coast. Engng 331–339.Google Scholar
29. Swart, D. H. 1974 Offshore sediment transport and equilibrium beach profiles. Delft Hydr. Lab. Publ. No. 131.Google Scholar
30. Tanaka, N., Sasaki, Y., Mowjood, M. I. M., Jinadasa, K. B. S. N. & Homchuen, S. 2007 Coastal vegetation structures and their function in tsunami protection: experience of the recent Indian Ocean tsunami. Landscape Ecol. Engng 3, 33–45.CrossRefGoogle Scholar
31. Thuy, N., Tanimoto, K., Tanaka, N., Harada, K. & Iimura, K. 2009 Effect of open gap in coastal forest on tsunami run-up – investigations by experiment and numerical simulation. Ocean Engng. 36, 1258–1269.CrossRefGoogle Scholar
32. Wolanski, E. 1992 Hydrodynamics of mangrove swamps and their coastal waters. Hydrobiologia 247, 141–161.CrossRefGoogle Scholar
33. Wolanski, E., Jones, M. & Bunt, J. S. 1980 Hydrodynamics of a tidal creek-mangrove swamp system. Austral. J. Mar. Freshwat. Res. 31, 431–450.CrossRefGoogle Scholar
34. Zhou, M. Y. & Sheng, P. 1989 First-principle calculation of dynamic permeability of porous media. Phy. Rev. B. 39, 12027–12039.CrossRefGoogle Scholar