Volume 11 Issue 4
Oct.  2018
Turn off MathJax
Article Contents
Article Navigation >  Water Science and Engineering  > 2018  >  11(4): 318-327
Ikha Magdalena, Iryanto, Dominic E. Reeve. 2018: Free-surface long wave propagation over linear and parabolic transition shelves. Water Science and Engineering, 11(4): 318-327. doi: 10.1016/j.wse.2019.01.001
Citation: Ikha Magdalena, Iryanto, Dominic E. Reeve. 2018: Free-surface long wave propagation over linear and parabolic transition shelves. Water Science and Engineering, 11(4): 318-327. doi: 10.1016/j.wse.2019.01.001
shu

Free-surface long wave propagation over linear and parabolic transition shelves

doi: 10.1016/j.wse.2019.01.001

  • a Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung 40132, Indonesia

  • b Informatics Department, Indramayu State Polytechnic, Indramayu 45252, Indonesia

  • c College of Engineering, Swansea University, Bay Campus, Swansea SA2 8PP, UK

Funds:  This work was supported by a Researcher Links Grant from the British Council, the Royal Academy of Engineering (Grant No. IAAP1/100086), and the EFRaCC Project funded through the British Council's Global Innovation Initiative Program.
More Information
  • Corresponding author: Dominic E. Reeve
  • Received Date: 2018-04-13
  • Rev Recd Date: 2018-09-19
    Abstract
  • Long-period waves pose a threat to coastal communities as they propagate from deep ocean to shallow coastal waters. At the coastline, such waves have a greater height and longer period in comparison with local storm waves, and can cause severe inundation and damage. In this study, we considered linear long waves in a two-dimensional (vertical-horizontal) domain propagating towards a shoreline over a shallowing shelf. New solutions to the linear shallow water equations were found, through the separation of variables, for two forms of transition shelf morphology: deep water and shallow coastal water horizontal shelves connected by linear and parabolic transition, respectively. Expressions for the transmission and reflection coefficients are presented for each case. The analytical solutions were used to test the results from a novel computational scheme, which was then applied to extending the existing results relating to the reflected and transmitted components of an incident wave. The solutions and computational package provide new tools for coastal managers to formulate improved defence and risk-mitigation strategies.

     

    • FullText(HTML)
  • loading
    • References(33)
  • Bautista,E.G., Arcos, E., Bautista, O.E., 2011. Propagation of ocean waves over a shelf with linear transition. Mechanica Computacional, (4), 225-242.
    Beji, S., Nadoaka, K., 1997. A time-dependent nonlinear mild slope equation for water waves.Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 453(1957),319-332. https://doi.org/10.1098/rspa.1997.0018.
    Bender, C.M., Orszag, S.A., 1978. Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill, New York.
    Berkhoff, J.C.W., 1972. Computation of combined refraction: Diffraction. In: Proceeding of 13th International Conference on Coastal Engineering, ASCE, pp. 55-69, https://doi.org/10.1061/9780872620490.027.
    Carrier, G.F., 1966.Gravity waves of water of variable depth. J. Fluid Mech.,24(4), 641-659. https://doi.org/10.1017/S0022112066000892.
    Copeland, G.J.M., 1985. A practical alternative to the mild-slope equation. Coastal Engineering, 9(2), 125-149. https://doi.org/10.1016/0378-3839(85)90002-X.
    Dalrymple, R.A., Suh, K.D., Kirby, J.T., Chae, J.W., 1989. Models for very wide-angle water waves and wave diffraction, Part 2: Irregular bathymetry. J. Fluid Mech., 201, 299-322. https://doi.org/10.1017/S0022112089000959.
    Ebersole, B.A., 1985. Refraction-diffraction model for linear water wave. Journal of Waterway, Port, Coastal, and Ocean Engineering, 111(6), 939-953. https://doi.org/10.1061/(ASCE)0733-950X(1985)111:6(939).
    Kajiura, K., 1961. On the partial reflection of water waves passing over a bottom of variable depth.In: Proceedings ofthe Tsunami Meetings 10th Pacific Science Congress, IUGG, pp.206-234.
    Kim, H.-S., Jung, B.-S., Lee, Y.-W., 2009. A linear wave equation over mild-sloped bed from double integration. Journal of the Korean Society for Marine Environment  & Enrgy, 12(3), 165-172.
    Kirby, J.T., 1986. On the gradual reflection of weakly nonlinear Stokes waves in regions of varying topography. J. Fluid Mech., 162, 187-209. https://doi.org/10.1017/S0022112086002008.
    Kowalik, Z., 1993. Solution of the linear shallow water equations by the fourth-order leapfrog scheme. JGR: Oceans, 98(C6), 10205-10209. https://doi.org/10.1029/93JC00652.
    Kowalik, Z., 2012. Introduction to Numerical Modeling of Tsunami Waves. University of Alaska, Fairbanks.
    Kristina, W., van Groesen, B., Bokhove, O., 2013. Modelling of tsunami wave run-up over sloping bathymetry using effective boundary conditions.  In: EGU Genereal Assembly Conference Abstracts, Vol. 15, p.453.
    Li, B., Anastasiou, K., 1992. Efficient elliptic solvers for the mild-slope equation using the multigrid technique. Coastal Engineering, 16(3), 245-266. https://doi.org/10.1016/0378-3839(92)90044-U.
    Li, B., Reeve, D.E., Fleming, C.A., 1993. Numerical solution of the elliptic mild-slope equation for irregular wave propagation. Coastal Engineering, 20(1-2),85-100. https://doi.org/10.1016/0378-3839(93)90056-E.
    Lin, P.Z., Liu, P.L.-F., 1998. A numerical study of breaking waves in the surf zone. J. Fluid Mech., 359, 239-264.             https://doi.org/10.1017/S002211209700846X.
    Madsen, P.A., Bingham, H.B., Liu, H., 2002. A new Boussinesq method for fully nonlinear waves from shallow to deep water, J. Fluid Mech., 462, 1-30. https://doi.org/10.1017/S0022112002008467.
    Magdalena, I., Erwina, N., Pudjaprasetya, S.R., 2015. Staggered momentum conservative scheme for radial dam break simulation. J. Sci. Comp., 65(3), 867-874. https://doi.org/10.1007/s10915-015-9987-5.
    Mei, C.C., Stiassne, M., Yue, D.K.-P., 2005. Theory and applications of ocean surface waves. In: Advanced Series on Ocean Engineering: Vol. 23, World Scientific. https://doi.org/10.1142/5566.
    Nielson, P. 1983. Analytical determination of nearshore wave height variation due to refraction, shoaling and friction. CoastalEngineering, 7(3), 233-251. https://doi.org/10.1016/0378-3839(83)90019-4.
    Nielson, P., 1984. Explicit solutions to practical wave problems. In: Proceedings of the International Conference of 19th Coastal Engineering Conference, Houston, pp. 968-982.
    Noviantri, V., Pudjaprasetya, S.R., 2010. The relevance of wavy beds as shoreline protection. In: Proceedings of 13th Asian Congress of Fluid Mechanics, pp.489-492.
    Nwogu, O., 1993. Alternative form of Boussinesq equations for nearshore wave propagation. Journal of Waterway,Port,Coastal, and Ocean Engineering, 119(6), 618-638. https://doi.org/10.1061/(ASCE)0733-950X(1993)119:6(618).
    Panchang, V., Cushman-Roisin, B., Pearce, B., 1988. Combined refraction-diffraction of short-waves in large coastal regions. Coastal Engineering, 12(2), 133-156. https://doi.org/10.1016/0378-3839(88)90002-6.
    Pudjaprasetya, S.R., Magdalena, I., 2014. Momentum conservative schemes for shallow water flows. East Asian Journal on Applied Mathematics, 4(2), 152-165.https://doi.org/10.4208/eajam.290913.170314a.
    Radder, A.C., 1979. On the parabolic equation method for water-wave propagation, J. Fluid Mech., 95(1), 159-176. https://doi.org/10.1017/S0022112079001397.
    Reeve, D.E., 1992. Bathymetric generation of an angular wave spectrum. Wave Motion, 16(3), 217-228. https://doi.org/10.1016/0165-2125(92)90030-6.
    Sadeghian, H., Peyman, B., 2012. Analytical solution of wave shoaling based on cnoidal wave theory. In: Proceedings of 9th International Conference on Coasts, Ports and Marine Structures, Tehran.
    Smith, R., Sprinks, T., 1975. Scattering of surface waves by a conical island. J. Fluid Mech., 72(2), 373-384. https://doi.org/10.1017/S0022112075003424.
    Stosius, R., Beyerle, G., Helm, A., Hoechner, A., Wickert, J., 2010. Simulation of space-borne tsunami detection using GNSS: Reflectometry applied to tsunamis in the Indian Ocean. Natural Hazards and Earth System Sciences, 10, 1359-1372. https://doi.org/10.5194/nhess-10-1359-2010.
    Suh, K.D., Dalrymple, R.A., Kirby, J.T., 1990, An angular spectrum model for propagation of Stokes waves, J. Fluid Mech., 221, 205-232. https://doi.org/10.1017/S0022112090003548.
    Synolakis, C.E., 1987. The runup of solitary waves. J. Fluid Mech., 185, 523-545. https://doi.org/10.1017/S002211208700329X.
    • Relative Articles
    • Supplements(0)
    • Cited By
  • 加载中

Catalog

    通讯作者: 陈斌, bchen63@163.com
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索
    Get Citation
    PDF
    XML

    Article Metrics

    Article views (413) PDF downloads(399) Cited by()
    Proportional views
    Related

    Copyright © 2009 Editorial office of Water Science and Engineering 苏ICP备12023610号-1

    Supported by: Beijing Renhe Information Technology Co. Ltd   support: info@rhhz.net

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return