Technical Papers
Jul 30, 2014

Optimal Collocation of Three Kinds of Bragg Breakwaters for Bragg Resonant Reflection by Long Waves

Publication: Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 141, Issue 3

Abstract

It is well known that, for a series of submerged artificial bars uniformly distributed in the coastal region parallel to the coastline, if the wavelength of the incident wave train is twice that of the bar distance, Bragg resonant reflection occurs. In this paper, three closed-form analytical solutions for linear long-wave reflection for bars with triangular shape, rectified cosinoidal shape, and idealized trapezoidal shape are presented. These analytical solutions show that the magnitude of the peak Bragg resonant reflection still depends on three bar parameters, which are the bar number, the dimensionless bar height, and the dimensionless bar width. Based on intensive analysis of the relations among these parameters, three sets of optimal curves to determine the optimal collocation of the three types of artificial bars are established, which may be very significant in the study of Bragg resonance and in the fundamental design of Bragg breakwaters.

Get full access to this article

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

Acknowledgments

This work is supported by the Natural Science Foundation of China (51369008), Guangxi Natural Science Foundation (2011GXNSFD018006), State Key Laboratory for Coast and Coastal Engineering (LP1303), and the Innovation Project of Guangxi Graduate Education (YCSZ2013059, JGY2014052, gxun-chx2013084). All the authors would like to gratefully acknowledge some useful suggestions and help from the two anonymous referees and from the editors.

References

Arscott, F. M. (1995). “Heun’s equation.” Heun’s differential equation, A. Ronveaux, ed., Oxford University Press, New York, 1–83.
Bender, C. J., and Dean, R. G. (2003). “Wave transformation by two-dimensional bathymetric anomalies with sloped transitions.” Coastal Eng., 50(1–2), 61–84.
Chang, H.-K., and Liou, J.-C. (2007). “Long wave reflection from submerged trapezoidal breakwaters.” Ocean Eng., 34(1), 185–191.
Cho, Y.-S., and Lee, C. (2000). “Resonant reflection of waves over sinusoidally varying topographies.” J. Coastal Res., 16(3), 870–876.
Cho, Y.-S., Lee, J.-I., and Kim, Y.-T. (2004). “Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem.” Ocean Eng., 31(10), 1325–1335.
Cho, Y.-S., Yoon, S. B., Lee, J.-T., and Yoon, T.-H. (2001). “A concept of beach protection with submerged breakwaters.” J. Coastal Res., 34(Special Issue), 671–678.
Dalrymple, R. A., and Kirby, J. T. (1986). “Water waves over ripples.” J. Waterway, Port, Coastal, Ocean Eng., 309–319.
Davies, A. G. (1982). “The reflection of wave energy by undulations on the seabed.” Dyn. Atmos. Oceans, 6(4), 207–232.
Davies, A. G., and Heathershaw, A. D. (1984). “Surface-wave propagation over sinusoidally varying topography.” J. Fluid Mech., 144, 419–443.
Dean, R. G. (1964). “Long wave modification by linear transitions.” J. Wtrwy. and Harb. Div., 90(1), 1–30.
Dingemans, M. W. (1997). Water wave propagation over uneven bottoms. Part 1—Linear wave propagation, World Scientific, Singapore, 141–143.
Guazzelli, E., Rey, V., and Belzons, M. (1992). “Higher-order Bragg reflection of gravity surface waves by periodic beds.” J. Fluid Mech., 245, 301–317.
Heathershaw, A. D. (1982). “Seabed-wave resonance and sand bar growth.” Nature, 296(5855), 343–345.
Hsu, T.-W., Chang, H.-K., and Tsai, L.-H. (2002). “Bragg reflection of waves by different shapes of artificial bars.” China Ocean Eng., 16(3), 21–30.
Hsu, T.-W., Hsiao, S.-C., Ou, S.-H., Wang, S.-K., Yang, B.-D., and Chou, S.-E. (2007). “An application of Boussinesq equations to Bragg reflection of irregular waves.” Ocean Eng., 34(5–6), 870–883.
Hsu, T.-W., Tsai, L.-H., and Huang, Y.-T. (2003). “Bragg scattering of water waves by multiply composite artificial bars.” Coastal Eng. J., 45(2), 235–253.
Jeon, C.-H., and Cho, Y.-K. (2006). “Bragg reflection of sinusoidal waves due to trapezoidal submerged breakwaters.” Ocean Eng., 33(14–15), 2067–2082.
Jung, T.-H., Suh, K.-D., Lee, S. O., and Cho, Y.-S. (2008). “Linear wave reflection by trench with various shapes.” Ocean Eng., 35(11–12), 1226–1234.
Kirby, J. T. (1986). “A general wave equation for waves over rippled beds.” J. Fluid Mech., 162, 171–186.
Kirby, J. T., and Anton, J. P. (1990). “Bragg reflection of waves by artificial bars.” Proc., 22nd Int. Conf. on Coastal Engineering, ASCE, New York, 757–768.
Lin, P., and Liu, H.-W. (2005). “Analytical study of linear long-wave reflection by a two-dimensional obstacle of general trapezoidal shape.” J. Eng. Mech., 822–830.
Liu, H.-W., Luo, J.-X., Lin, P., and Liu, R. (2013). “Analytical solution for long-wave reflection by a general breakwater or trench with curvilinear slopes.” J. Eng. Mech., 229–245.
Liu, H.-W., Yang, J., and Lin, P. (2012). “An analytic solution to the modified mild-slope equation for wave propagation over one-dimensional piecewise smooth topographies.” Wave Motion, 49(3), 445–460.
Mei, C. C. (1985). “Resonant reflection of surface water waves by periodic sandbars.” J. Fluid Mech., 152, 315–335.
Mei, C. C., Hara, T., and Naciri, M. (1988). “Note on Bragg scattering of water waves by parallel bars on the seabed.” J. Fluid Mech., 186, 147–162.
Miles, J. (1981). “Oblique surface-wave diffraction by a cylindrical obstacle.” Dyn. Atmos. Oceans, 6(2), 121–123.
Miles, J. (1990). “Wave reflection from a gently sloping beach.” J. Fluid Mech., 214, 59–66.
Naciri, M., and Mei, C. C. (1988). “Bragg scattering of water waves by a doubly periodic seabed.” J. Fluid Mech., 192, 51–74.
Renzi, E., and Sammarco, P. (2010). “Landslide tsunamis propagating around a conical island.” J. Fluid Mech., 650, 251–285.
Tsai, L.-H., Kuo, Y.-S., Lan, Y.-J., Hsu, T.-W., and Chen, W.-J. (2011). “Investigation of multiply composite artificial bars for Bragg scattering of water waves.” Coastal Eng. J., 53(4), 521–548.
Wang, S.-K., Hsu, T.-W., Tsai, L.-H., and Chen, S.-H. (2006). “An application of Miles’ theory to Bragg scattering of water waves by doubly composite artificial bars.” Ocean Eng., 33(3–4), 331–349.
Zhang, L., Kim, M. H., Zhang, J., and Edge, B. L. (1999). “Hybrid model for Bragg scattering of water waves by steep multiply-sinusoidal bars.” J. Coastal Res., 15(2), 486–495.

Information & Authors

Information

Published In

Go to Journal of Waterway, Port, Coastal, and Ocean Engineering
Journal of Waterway, Port, Coastal, and Ocean Engineering
Volume 141Issue 3May 2015

History

Received: Jan 13, 2014
Accepted: Jun 19, 2014
Published online: Jul 30, 2014
Published in print: May 1, 2015

Permissions

Request permissions for this article.

Authors

Affiliations

Huan-Wen Liu [email protected]
Professor, School of Sciences, Guangxi Univ. for Nationalities, Nanning, Guangxi 530006, P.R. China (corresponding author). E-mail: [email protected]
Heng Luo
M.Sc. Candidate, School of Sciences, Guangxi Univ. for Nationalities, Nanning, Guangxi 530006, P.R. China.
Hui-Dan Zeng
M.Sc. Candidate, School of Sciences, Guangxi Univ. for Nationalities, Nanning, Guangxi 530006, P.R. China.

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