TECHNICAL PAPERS
Sep 1, 2007

Numerical Study of Solitary Wave Interaction with Porous Breakwaters

Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 133, Issue 5

Abstract

Solitary wave interaction with porous breakwaters is studied by using a two-dimensional numerical model. In this model, flows outside of porous media are described by Reynolds-averaged Navier-Stokes equations. For porous flows, the spatially averaged Navier-Stokes equations, in which the effect of porous media is considered by including additional inertia and drag forces, are derived and implemented. The drag force is modeled according to Morison’s equation assuming uniform spherical particles within porous media. The corresponding drag force coefficient is expressed as the function of Reynolds number and hence the proposed porous flow model is valid in a wide range of porous flow regimes, i.e., laminar (linear friction), transitional, and turbulent (nonlinear friction) flows. The numerical model is validated against available theories and experimental data for both long wave and solitary wave interaction with porous breakwaters. The model is then employed to study solitary wave interaction with fully emerged rectangular porous breakwaters with different length and particle size. Based on the results, the characteristics of wave reflection, transmission and energy dissipation are discussed. Additional numerical tests are conducted to study the effects of depth of submergence and porosity of breakwaters on wave transformation. The scale effects in small scale and large scale model tests are also discussed by performing numerical experiments in the reduced and enlarged numerical wave flumes.

Get full access to this article

View all available purchase options and get full access to this article.

Acknowledgments

The study was supported, in part, by the research grants provided by Defence Science and Technology Agency (DSTA), Singapore (No. R-347-000-021-422) and National Natural Science Foundation of China (NSFC Nos. 50525926 and 50679046).

References

Anderson, O. H. (1994). “Flow in porous media with special reference to breakwater structures.” Ph.D. thesis, Aalborg Univ., Aalborg, Denmark.
Burcharth, H. F., and Anderson, O. H. (1995). “On the one-dimensional steady and unsteady porous flow equations.” Coastal Eng., 24, 233–257.
Burcharth, H. F., Liu, Z., and Troch, P. (1999). “Scaling of core material in rubble mound breakwater model tests.” Proc., 5th COPEDEC, Cape Town, South Africa, 1518–1528.
Carman, P. C. (1937). “Fluid flow through granular beds.” Trans. Inst. Chem. Eng., 15, 150–166.
Chang, K.-A., Hsu, T.-J., and Liu, P. L.-F. (2001). “Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle. 1: Solitary waves.” Coastal Eng., 44, 13–26.
Dalrymple, R. A., Losada, M. A., and Martin, P. A. (1991). “Reflection and transmission from porous structures under oblique wave attack.” J. Fluid Mech., 224, 625–644.
Dattatri, J., Raman, H., and Shankar, N. J. (1978). “Performance characteristics of submerged breakwaters.” Proc., 16th Int. Conf. on Coastal Engineering, ASCE, New York, 2153–2171.
Engelund, F. (1953). “On the laminar and turbulent flows of ground water through homogeneous sand.” Transactions of the Danish Academy of Technical Sciences, 3(4), 7–105.
Ergun, S. (1952). “Fluid flow through packed columns.” Chem. Eng. Prog., 48(2), 89–94.
Fair, G. M., Geyer, J. C., and Okum, D. A. (1968). Water purification and wastewater treatment and disposal, Vol. 2, Waste Water Management, Wiley, New York.
Golshani, A., Mizutani, N., Hur, D.-S., and Shimizu, H. (2003). “Three-dimensional analysis of nonlinear interaction between water waves and vertical permeable breakwater.” Coast. Eng. Japan, 45(1), 1–28.
Goring, D. G. (1978). “Tsunamis—The propagation of long waves onto a shelf.” Rep. No. KH-R-38, W. M. Keck Laboratory of Hydr. and Wat. Res., California Institute of Technology, Pasadena, Calif.
Grilli, S. T., Losada, M. A., and Martin, F. (1994). “Characteristics of solitary wave breaking induced by breakwaters.” J. Waterway, Port, Coastal, Ocean Eng., 120(1), 74–92.
Gu, Z. (1990). “Water wave interaction with porous structures of irregular cross sections.” Ph.D. dissertation, Univ. of Florida, Gainesville, Fla.
Huang, C.-J., Chang, H.-H., and Hwung, H.-H. (2003). “Structural permeability effects on the interaction of a solitary wave and a submerged breakwater.” Coastal Eng., 49, 1–24.
Huang, C.-J., and Dong, C.-M. (2001). “On the interaction of a solitary wave and a submerged dike.” Coastal Eng., 43, 265–286.
Isaacson, M., Baldwin, J., Allyn, N., and Cowdell, S. (2000). “Wave interactions with perforated breakwater.” J. Waterway, Port, Coastal, Ocean Eng., 126(5), 229–235.
Karunarathna, S. A. S. A., and Lin, P. (2006). “Numerical simulation of wave damping over porous seabeds.” Coastal Eng., 53, 845–855.
Kondo, H., and Toma, S. (1972). “Reflection and transmission for a porous structure.” Proc., 13th Int. Conf. Coastal Engineering, ASCE, New York, 1847–1865.
Lamb, H. (1932). Hydrodynamics, 6th Ed., Dover, New York.
Lin, P. (2004). “A numerical study of solitary wave interaction with rectangular obstacles.” Coastal Eng., 51, 35–51.
Lin, P. (2007). Numerical modeling of water waves, Taylor & Francis Group, London.
Lin, P., and Liu, P. L.-F. (1998). “A numerical study of breaking waves in the surf zone.” J. Fluid Mech., 359, 239–264.
Lin, P., and Liu, P. L.-F. (1999). “Internal wavemaker for Navier-Stokes equations models.” J. Waterway, Port, Coastal, Ocean Eng., 125(4), 207–215.
Liu, P. L.-F., and Lin, P. (1997). “A numerical model for breaking wave: The volume of fluid method.” Research Rep. No. CACR-97-02, Ctr. for Appl. Coast. Res., Oc. Eng. Lab., Univ. of Delaware, Newark, Del.
Liu, P. L.-F., Lin, P., Chang, K.-A., and Sakakiyama, T. (1999). “Numerical modeling of wave interaction with porous structures.” J. Waterway, Port, Coastal, Ocean Eng., 125(6), 322–330.
Liu, P. L.-F., and Wen, J. (1997). “Nonlinear diffusive surface waves in porous media.” J. Fluid Mech., 347, 119–139.
Losada, M. A., Vidal, C., and Medina, R. (1989). “Experimental study of the evolution of a solitary wave at an abrupt junction.” J. Geophys. Res., 94(C10), 14557–14566.
Lynett, P. J., Liu, P. L.-F., Losada, I. J., and Vidal, C. (2000). “Solitary wave interaction with porous breakwaters.” J. Waterway, Port, Coastal, Ocean Eng., 126(6), 314–322.
Madsen, O. S. (1974). “Wave transmission through porous structures.” J. Wtrwy., Harb. and Coast. Engrg. Div., 100(3), 169–188.
Madsen, O. S., and White, S. M. (1975). “Reflection and transmission characteristics of porous rubble mound breakwaters.” Rep. No., 207, The U.S. Army, Coastal Engineering Res. Center.
Mallayachari, V., and Sundar, V. (1994). “Reflection characteristics of permeable seawalls.” Coastal Eng., 23, 135–150.
Miles, J. W. (1979). “On the Kortweg-de Vries equation for a gradually varying channel.” J. Fluid Mech., 91, 181–190.
Seabra-Santos, F. J., Renouard, D. P., and Temperville, A. M. (1987). “Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle.” J. Fluid Mech., 176, 117–134.
Silva, R., Losada, I. J., and Losada, M. A. (2000). “Reflection and transmission of tsunami waves by coastal structures.” Appl. Ocean. Res., 22(4), 215–223.
Sollitt, C. K., and Cross, R. H. (1972). “Wave transmission through permeable breakwaters.” Proc., 13th Int. Conf. on Coastal Engineering, ASCE, New York, 1827–1846.
Su, X., and Lin, P. (2005). “A hydrodynamic study on flow motion with vegetation.” Mod. Phys. Lett. B, 19(28–29), 1659–1662.
Sulisz, W. (1985). “Wave reflection and transmission at permeable breakwaters of arbitrary cross-section.” Coastal Eng., 9, 371–386.
Ting, C.-L., Lin, M.-C., and Cheng, C.-Y. (2004). “Porosity effects on nonbreaking surface waves over permeable submerged breakwaters.” Coastal Eng., 50, 213–224.
Troch, P., and de Rouck, J. (1999). “Development of two-dimensional numerical wave flume for wave interaction with rubble mound breakwaters.” Proc., 26th Int. Conf. on Coastal Engineering, ASCE, Reston, Va, 1638–1649.
Twu, S.-W., and Chieu, C.-C. (2000). “A highly wave dissipation offshore breakwater.” Ocean Eng., 27, 315–330.
Twu, S.-W., Liu, C.-C., and Twu, C.-W. (2002). “Wave damping characteristics of vertically stratified porous structures under oblique wave action.” Ocean Eng., 29, 1295–1311.
Van Gent, M. R. A. (1995). “Wave interaction of permeable coastal structures.” Ph.D. thesis, Delft Univ., Delft, The Netherlands.
Van Gent, M. R. A., Tönjes, P., Petit, H. A. H., and Van den Bosch, P. (1995). “Wave action on and in permeable structures.” Proc., 24th Int. Conf. on Coastal Engineering, ASCE, 1739–1753.
Vidal, C., Losada, M. A., Medina, R., and Rubio, J. (1988). “Solitary wave transmission through porous breakwaters.” Proc., 21st Int. Conf. on Coastal Engineering, ASCE, Costa del Sol-Malaga, Spain, 1073–1083.
Ward, J. C. (1964). “Turbulent flow in porous media.” J. Hydr. Div., 90(5), 1–12.
Wilson, K. W., and Cross, R. H. (1972). “Scale effects in rubble-mound breakwaters.” Proc., 13th Int. Conf. on Coastal Engineering, ASCE, Vancouver, B.C., Canada, 1873–1884.
Wurjanto, A., and Kobayashi, N. (1993). “Irregular wave reflection and run up on permeable slopes.” J. Waterway, Port, Coastal, Ocean Eng., 119(5), 537–557.
Yasuda, T., and Hara, M. (1991). “Breaking and reflection of a steep solitary wave caused by a submerged obstacle.” Proc., 22nd Int. Conf. on Coastal Engineering, ASCE, New York, 923–934.
Yu, X., and Chwang, A. T. (1994). “Wave motion through porous structures.” J. Eng. Mech., 120(5), 989–1008.

Information & Authors

Information

Published In

Go to Journal of Waterway, Port, Coastal, and Ocean Engineering
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 133Issue 5September 2007
Pages: 352 - 363

History

Received: Dec 20, 2005
Accepted: May 10, 2006
Published online: Sep 1, 2007
Published in print: Sep 2007

Permissions

Request permissions for this article.

Authors

Affiliations

Pengzhi Lin
State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan Univ., Chengdu, China (corresponding author).
S. A. Karunarathna
Dept. of Civil Engineering, National Univ. of Singapore, Singapore 117576, Singapore.

Metrics & Citations

Metrics

Citations

Download citation

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

Cited by

View Options

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Get Access

Access content

Please select your options to get access

Log in/Register Log in via your institution (Shibboleth)
ASCE Members: Please log in to see member pricing

Purchase

Save for later Information on ASCE Library Cards
ASCE Library Cards let you download journal articles, proceedings papers, and available book chapters across the entire ASCE Library platform. ASCE Library Cards remain active for 24 months or until all downloads are used. Note: This content will be debited as one download at time of checkout.

Terms of Use: ASCE Library Cards are for individual, personal use only. Reselling, republishing, or forwarding the materials to libraries or reading rooms is prohibited.
ASCE Library Card (5 downloads)
$105.00
Add to cart
ASCE Library Card (20 downloads)
$280.00
Add to cart
Buy Single Article
$35.00
Add to cart

Media

Figures

Other

Tables

Share

Share

Copy the content Link

Share with email

Email a colleague

Share