Wave propagation passing over a submerged porous breakwater
A linear model of waves propagating over a submerged porous breakwater is derived from two coupled boundary-value problems, each of which represents the governing equation in a different medium. The model is similar to the shallow-water equations (SWE), with a damping term proportional to the character of the porous breakwater. Therefore, waves traveling above the breakwater will be absorbed, and the amplitude decreases. The wave propagation passing over the submerged breakwater for monochromatic and solitary waves is analyzed. For monochromatic waves, the numerical solution agrees with the analytical. The amplitude decreases exponentially with respect to the space variable in the region above the breakwater. The reflected wave is also analyzed when the model is combined with a model using the shallow-water equations.
KeywordsDarcy’s law Potential function Shallow-water equations (SWE) Submerged porous breakwater
Unable to display preview. Download preview PDF.
- 3.van Groesen E, Andonowati (2002) Similarities between optic and surface water waves. J Indones Math Soc 8: 1–8Google Scholar
- 11.Solitt CK, Cross RH (1972) Wave transmission through permeable breakwaters. In: Proceedings of 13th international conference on Coastal engineering, Vancouver, pp 1837–1846Google Scholar
- 12.Madsen OS (1974) Wave transmission through porous structures. J Waterw Harbors Coast Eng 100: 169–188Google Scholar
- 13.Rojanakamthorn S, Isobe M, Watanabe A (1989) A mathematical model of wave transformation over a submerged breakwater. Coast Eng Jpn 31: 209–234Google Scholar
- 17.Wiryanto LH (2010) Unsteady waves generated by flow over a porous layer. Int J Appl Math (accepted)Google Scholar
- 19.Wiryanto LH, Anwarus S (2009) Monochromatic waves over permeable bed. In: Proceedings of 5th Asian Mathematical Conference, Kuala Lumpur, Malaysia, pp 617–622Google Scholar