Wave reflection by a submerged cycloidal breakwater in presence of a beach with different depth profiles

Wiegel, 1964 Lamb, 1932 Bartholomeusz, 1958, The reflexion of long waves at a step, J. Eng. Mech. ASCE, 54, 106 Mei, 1997 Dingemans, 2005 Chang, 2004, Long wave reflection and transmission over a sloping step, China Ocean Eng., 18, 371 Chang, 2007, Long wave reflection from submerged trapezoidal breakwaters, Ocean Eng., 34, 185, 10.1016/j.oceaneng.2005.11.017 Lin, 2005, Analytical study of linear long-wave reflection by a two-dimensional obstacle of general trapezoidal shape, J. Eng. Mech. ASCE, 131, 822, 10.1061/(ASCE)0733-9399(2005)131:8(822) Bragg, 1913, The reflection of x-rays by crystals, Proc. R. Soc. A, 88, 428 Davies, 1984, Surface-wave propagation over sinusoidally varying topography, J. Fluid Mech., 144, 419, 10.1017/S0022112084001671 Mei, 1985, Resonant reflection of surface water waves by periodic sand bars, J. Fluid Mech., 152, 315, 10.1017/S0022112085000714 Ouyang, 2016, Bragg reflection of water waves by multiple submerged semi-circular breakwaters, J. Hydro-Environ. Res., 11, 91, 10.1016/j.jher.2015.06.004 Jiang, 2017, Wave load on submerged quarter-circular and semicircular breakwaters under irregular waves, Coastal Eng., 121, 265, 10.1016/j.coastaleng.2016.11.006 Ji, 2017, Wave transformation over submerged breakwaters by the constrained interpolation profile method, Ocean Eng., 136, 294, 10.1016/j.oceaneng.2017.03.037 Zeng, 2017, Optimal collocation of bragg breakwaters with rectangular bars on sloping seabed for bragg resonant reflection by long waves, Ocean Eng., 130, 156, 10.1016/j.oceaneng.2016.11.066 J. Berkhoff, Computation of combined refraction - diffraction, in: Proceedings of the 13th International Conference on Coastal Engineering ASCE, Vancouver, Canada, 1972, pp. 471–490. Chamberlain, 1995, The modified mild-slope equation, J. Fluid Mech., 291, 393, 10.1017/S0022112095002758 Kirby, 1986, A general wave equation for waves over rippled beds, J. Fluid Mech., 162, 171, 10.1017/S0022112086001994 Dean, 1984 Hsiao, 2010, An analytical solution to the modified mild-slope equation for waves propagating around a circular conical island, J. Mar. Sci. Technol., 18, 520, 10.51400/2709-6998.1905 Cheng, 2011, A new solution for waves incident to a circular island on an axi-symmetric shoal, Ocean Eng., 18, 1916, 10.1016/j.oceaneng.2011.09.026 Liu, 2012, An analytic solution to the modified mild-slope equation for wave propagation over one-dimensional piecewise smooth topographies, Wave Motion, 18, 445, 10.1016/j.wavemoti.2012.01.002 Jung, 2008, Linear wave reflection by trench with various shapes, Ocean Eng., 35, 1226, 10.1016/j.oceaneng.2008.04.001 Xie, 2012, An exact analytic solution to the modified mild-slope equation for waves propagating over a trench with various shapes, Ocean Eng., 50, 72, 10.1016/j.oceaneng.2012.05.014 Medina-Rodríguez, 2016, Propagation of linear long water waves on a cycloidal breakwater, J. Eng. Math., 100, 187, 10.1007/s10665-015-9841-7 Barbosa-López, 2019, Wave reflection by a submerged cycloidal breakwater using the modified mild-slope equation, Ocean Eng., 176, 144, 10.1016/j.oceaneng.2019.02.044 Yang, 2011 Sezer, 1996, A method for the approximate solution of the second-order linear differential equations in terms of taylor polynomials, Int. J. Math. Educ. Sci. Technol., 27, 821, 10.1080/0020739960270606 Lin, 2005, Analytical study of linear long-wave reflection by a two-dimensional obstacle of general trapezoidal shape, J. Eng. Mech., 131, 822, 10.1061/(ASCE)0733-9399(2005)131:8(822) Liu, 2015, Optimization of parabolic bars for maximum bragg resonant reflection of long waves, J. Hydrodyn., 27, 373, 10.1016/S1001-6058(15)60495-4 Booij, 1983, A note on the accuracy of the mild-slope equation, Coastal Eng., 7, 191, 10.1016/0378-3839(83)90017-0 Liu, 2013, Analytical solution for long-wave reflection by a general breakwater or trench with curvilinear slopes, J. Eng. Mech., 139, 229, 10.1061/(ASCE)EM.1943-7889.0000483 Newman, 1965, Propagation of water waves past long two-dimensional obstacles, J. Fluid Mech., 23, 23, 10.1017/S0022112065001210 Xie, 2011, Analytical solution for long-wave reflection by a rectangular obstacle with two scour trenches, J. Eng. Mech., 137, 919, 10.1061/(ASCE)EM.1943-7889.0000293