Cerrato, Antonio González, José A. and Rodríguez-Tembleque, Luis 2016. Boundary element formulation of the Mild-Slope equation for harmonic water waves propagating over unidirectional variable bathymetries. Engineering Analysis with Boundary Elements, Vol. 62, p. 22.
Liu, Huan-Wen Yang, Jing and Lin, Pengzhi 2012. An analytic solution to the modified mild-slope equation for wave propagation over one-dimensional piecewise smooth topographies. Wave Motion, Vol. 49, Issue. 3, p. 445.
Das, S. and Bora, S.N. 2014. Reflection of oblique ocean water waves by a vertical rectangular porous structure placed on an elevated horizontal bottom. Ocean Engineering, Vol. 82, p. 135.
Liu, Huan-Wen Wang, Qiu-Yue and Tang, Guo-Ji 2013. Exact Solution to the Modified Mild-Slope Equation for Wave Scattering by a Cylinder with an Idealized Scour Pit. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 139, Issue. 5, p. 413.
Kim, J. W. Ertekin, R. C. and Bai, K. J. 2010. Linear and Nonlinear Wave Models Based on Hamilton’s Principle and Stream-Function Theory: CMSE and IGN. Journal of Offshore Mechanics and Arctic Engineering, Vol. 132, Issue. 2, p. 021102.
Jung, Tae-Hwa and Suh, Kyung-Duck 2008. An analytical solution to the extended mild-slope equation for long waves propagating over an axi-symmetric pit. Wave Motion, Vol. 45, Issue. 6, p. 835.
Liu, Huan-Wen Lin, Pengzhi and Shankar, N.Jothi 2004. An analytical solution of the mild-slope equation for waves around a circular island on a paraboloidal shoal. Coastal Engineering, Vol. 51, Issue. 5-6, p. 421.
Xie, Jian-Jian and Liu, Huan-Wen 2013. Analytical study for linear wave transformation by a trapezoidal breakwater or channel. Ocean Engineering, Vol. 64, p. 49.
Seo, Seung-Nam 2014. Transfer matrix of linear water wave scattering over a stepwise bottom. Coastal Engineering, Vol. 88, p. 33.
Liu, Huan-Wen and Xie, Jian-Jian 2013. The series solution to the modified mild-slope equation for wave scattering by Homma islands. Wave Motion, Vol. 50, Issue. 4, p. 869.
Tsai, Chia-Cheng Lin, Zhong-Han and Hsu, Tai-Wen 2015. Using a local radial basis function collocation method to approximate radiation boundary conditions. Ocean Engineering, Vol. 105, p. 231.
Belibassakis, Kostas A. 2012. Water-wave induced groundwater pressure and flow in variable bathymetry regions and sandy beaches by an enhanced coupled-mode model. Ocean Engineering, Vol. 47, p. 104.
Chamberlain, P. G. and Porter, D. 1996. Approximations to wave trapping by topography. Journal of Fluid Mechanics, Vol. 325, Issue. -1, p. 357.
Belibassakis, Konstadinos A. 2000. The Green’s function of the mild-slope equation:. Wave Motion, Vol. 32, Issue. 4, p. 339.
Manam, S.R. and Kaligatla, R.B. 2012. A mild-slope model for membrane-coupled gravity waves. Journal of Fluids and Structures, Vol. 30, p. 173.
Liu, Ying-Zhong and Shi, John Z. 2008. A theoretical formulation for wave propagations over uneven bottom. Ocean Engineering, Vol. 35, Issue. 3-4, p. 426.
Maa, Jerome Peng-Yea Tsai, Cheng-Han Juang, Wen-Jye and Tseng, Hsiang-Maw 2011. A preliminary study on Typhoon Tim induced resonance at Hualien Harbor, Taiwan. Ocean Dynamics, Vol. 61, Issue. 4, p. 411.
Williams, Pete and Ehrenmark, Ulf 2010. A note on the use of a new dispersion formula for wave transformation over Roseau's curved beach profile. Wave Motion, Vol. 47, Issue. 8, p. 641.
Liu, Huan-Wen Fu, Dan-Juan and Sun, Xiao-Ling 2013. Analytic Solution to the Modified Mild-Slope Equation for Reflection by a Rectangular Breakwater with Scour Trenches. Journal of Engineering Mechanics, Vol. 139, Issue. 1, p. 39.
Das, Santu and Bora, Swaroop Nandan 2014. Wave damping by a vertical porous structure placed near and away from a rigid vertical wall. Geophysical & Astrophysical Fluid Dynamics, Vol. 108, Issue. 2, p. 147.
Griffiths, L.S. and Porter, R. 2012. Focusing of surface waves by variable bathymetry. Applied Ocean Research, Vol. 34, p. 150.
Athanassoulis, G. A. and Papoutsellis, Ch. E. 2017. Exact semi-separation of variables in waveguides with non-planar boundaries. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, Vol. 473, Issue. 2201, p. 20170017.
Silva, R. Losada, M.A. and Salles, P. 2006. Modelling linear wave transformation induced by dissipative structures—Random waves. Ocean Engineering, Vol. 33, Issue. 16, p. 2174.
Zhai, Xi-Yuan Liu, Huan-Wen and Xie, Jian-Jian 2013. Analytic study to wave scattering by a general Homma island using the explicit modified mild-slope equation. Applied Ocean Research, Vol. 43, p. 175.
Liao, Shijun 2014. Do peaked solitary water waves indeed exist?. Communications in Nonlinear Science and Numerical Simulation, Vol. 19, Issue. 6, p. 1792.
Toledo, Y. Hsu, T.-W. and Roland, A. 2012. Extended time-dependent mild-slope and wave-action equations for wave-bottom and wave-current interactions. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 468, Issue. 2137, p. 184.
Suh, Kyung Doug Lee, Changhoon and Park, Woo Sun 1997. Time-dependent equations for wave propagation on rapidly varying topography. Coastal Engineering, Vol. 32, Issue. 2-3, p. 91.
Behera, Harekrushna Sahoo, Trilochan and Ng, Chiu-On 2016. Wave Scattering by a Partial Flexible Porous Barrier in the Presence of a Step-Type Bottom Topography. Coastal Engineering Journal, Vol. 58, Issue. 03, p. 1650008.
Silva, R. Mendoza, E. and Losada, M.A. 2006. Modelling linear wave transformation induced by dissipative structures—Regular waves. Ocean Engineering, Vol. 33, Issue. 16, p. 2150.
Diaz-Hernandez, Gabriel Losada, Inigo J. and Mendez, Fernando J. 2017. Improving construction management of port infrastructures using an advanced computer-based system. Automation in Construction, Vol. 81, p. 122.
Zhu, Shutang 2001. Water waves within a porous medium on an undulating bed. Coastal Engineering, Vol. 42, Issue. 1, p. 87.
Staziker, D.J. Porter, D. and Stirling, D.S.G. 1996. The scattering of surface waves by local bed elevations. Applied Ocean Research, Vol. 18, Issue. 5, p. 283.
Kaligatla, R. B. and Manam, S. R. 2016. Bragg resonance of membrane-coupled gravity waves over a porous bottom. International Journal of Advances in Engineering Sciences and Applied Mathematics, Vol. 8, Issue. 3, p. 222.
Silva, R. Salles, P. and Govaere, G. 2003. Extended solution for waves travelling over a rapidly changing porous bottom. Ocean Engineering, Vol. 30, Issue. 4, p. 437.
Kim, Hyoseob and Jang, Changhwan 2013. Water wave propagation equation from expanded form of Leibniz rule. KSCE Journal of Civil Engineering, Vol. 17, Issue. 2, p. 257.
Tsai, Chia-Cheng Hsu, Tai-Wen and Lin, Yueh-Ting 2011. On Step Approximation for Roseau's Analytical Solution of Water Waves. Mathematical Problems in Engineering, Vol. 2011, p. 1.
Tsai, Chia-Cheng Lin, Yueh-Ting Chang, Jen-Yi and Hsu, Tai-Wen 2016. A coupled-mode study on weakly viscous Bragg scattering of surface gravity waves. Ocean Engineering, Vol. 122, p. 136.
Zhu, S.-P. and Noor-Harun, F. 2009. Refraction of interfacial waves over a circular hump. Proceedings of the Institution of Civil Engineers - Engineering and Computational Mechanics, Vol. 162, Issue. 4, p. 199.
Maa, J.P.-Y. Hsu, T.-W. and Lee, D.-Y. 2002. The RIDE model: an enhanced computer program for wave transformation. Ocean Engineering, Vol. 29, Issue. 11, p. 1441.
Maa, Jerome P-Y. Hobbs, Carl H. Kim, S. C. and Wei, Eugene 2004. Potential Impacts of Sand Mining Offshore of Maryland and Delaware: Part 1—Impacts on Physical Oceanographic Processes. Journal of Coastal Research, Vol. 201, p. 44.
Chuang, Shih-Hsuan Yueh, Ching-Yun and Huang, Liang-Hsiung 2015. Dual boundary element model coupled with the dual reciprocity method to determine wave scattering by a concentric cylindrical system mounted on a conical shoal. Engineering Analysis with Boundary Elements, Vol. 56, p. 30.
Lin, Pengzhi and Liu, Huan-Wen 2007. Scattering and Trapping of Wave Energy by a Submerged Truncated Paraboloidal Shoal. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 133, Issue. 2, p. 94.
Manam, Srinivasa R. Toledo, Yaron and Agnon, Yehuda 2011. Complementary mild-slope equations in a two-layer fluid. Wave Motion, Vol. 48, Issue. 3, p. 223.
Couston, Louis-Alexandre Jalali, Mir Abbas and Alam, Mohammad-Reza 2017. Shore protection by oblique seabed bars. Journal of Fluid Mechanics, Vol. 815, p. 481.
Xie, Jian-Jian and Liu, Huan-Wen 2012. An exact analytic solution to the modified mild-slope equation for waves propagating over a trench with various shapes. Ocean Engineering, Vol. 50, p. 72.
Herbers, T. H. C. Hendrickson, E. J. and O'Reilly, W. C. 2000. Propagation of swell across a wide continental shelf. Journal of Geophysical Research: Oceans, Vol. 105, Issue. C8, p. 19729.
Alvarez, Amaury C. García, Galina C. and Sarkis, Marcus 2017. The ultra weak variational formulation for the modified mild-slope equation. Applied Mathematical Modelling, Vol. 52, p. 28.
Liao, Bo Cao, Dun-Qian and Liu, Huan-Wen 2014. Wave transformation by a dredge excavation pit for waves from shallow water to deep water. Ocean Engineering, Vol. 76, p. 136.
Kuo, Yu-Shu Hsu, Tai-Wen Tsai, Chia-Cheng and Huang, Yu-Hsuan 2012. An Extended Analytic Solution of Combined Refraction and Diffraction of Long Waves Propagating over Circular Island. Journal of Applied Mathematics, Vol. 2012, p. 1.
Kaligatla, R. B. Manisha and Sahoo, T. 2017. Wave trapping by dual porous barriers near a wall in the presence of bottom undulation. Journal of Marine Science and Application, Vol. 16, Issue. 3, p. 286.
Cerrato, Antonio Rodríguez-Tembleque, Luis González, José A. and Ferri Aliabadi, M.H. 2017. A coupled finite and boundary spectral element method for linear water-wave propagation problems. Applied Mathematical Modelling, Vol. 48, p. 1.
Tsoukala, V.K. Katsardi, V. and Belibassakis, K.A. 2014. Wave transformation through flushing culverts operating at seawater level in coastal structures. Ocean Engineering, Vol. 89, p. 211.
Behera, H. Kaligatla, R.B. and Sahoo, T. 2015. Wave trapping by porous barrier in the presence of step type bottom. Wave Motion, Vol. 57, p. 219.
Belibassakis, K.A. Athanassoulis, G.A. and Gerostathis, Th.P. 2001. A coupled-mode model for the refraction–diffraction of linear waves over steep three-dimensional bathymetry. Applied Ocean Research, Vol. 23, Issue. 6, p. 319.
Magne, R. Belibassakis, K. A. Herbers, T. H. C. Ardhuin, Fabrice O'Reilly, W. C. and Rey, V. 2007. Evolution of surface gravity waves over a submarine canyon. Journal of Geophysical Research, Vol. 112, Issue. C1,
Hsiao, Sung-Shan Chang, Chun-Ming and Wen, Chih-Chung 2009. Solution for wave propagation through a circular cylinder mounted on different topography ripple-bed profile shoals using DRBEM. Engineering Analysis with Boundary Elements, Vol. 33, Issue. 11, p. 1246.
TOLEDO, YARON and AGNON, YEHUDA 2010. A scalar form of the complementary mild-slope equation. Journal of Fluid Mechanics, Vol. 656, p. 407.
Chandrasekera, Carmela N. and Cheung, Kwok Fai 2001. Linear Refraction-Diffraction Model for Steep Bathymetry. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 127, Issue. 3, p. 161.
Chandrasekera, Carmela N. and Cheung, Kwok Fai 1997. Extended Linear Refraction-Diffraction Model. Journal of Waterway, Port, Coastal, and Ocean Engineering, Vol. 123, Issue. 5, p. 280.
Ehrenmark, U.T and Williams, P.S 2001. Wave parameter tuning for the application of the mild-slope equation on steep beaches and in shallow water. Coastal Engineering, Vol. 42, Issue. 1, p. 17.
Zhu, Shutang and Chwang, Allen T. 2001. Analytical Study of Porous Wave Absorber. Journal of Engineering Mechanics, Vol. 127, Issue. 4, p. 326.
Naserizadeh, R. Bingham, Harry B. and Noorzad, A. 2011. A coupled boundary element-finite difference solution of the elliptic modified mild slope equation. Engineering Analysis with Boundary Elements, Vol. 35, Issue. 1, p. 25.
Liu, Huan-Wen and Zhou, Xiao-Mei 2014. Explicit modified mild-slope equation for wave scattering by piecewise monotonic and piecewise smooth bathymetries. Journal of Engineering Mathematics, Vol. 87, Issue. 1, p. 29.
Toledo, Yaron 2013. The oblique parabolic equation model for linear and nonlinear wave shoaling. Journal of Fluid Mechanics, Vol. 715, p. 103.
Silva, Rodolfo Borthwick, Alistair G.L. and Taylor, Rodney Eatock 2005. Numerical implementation of the harmonic modified mild-slope equation. Coastal Engineering, Vol. 52, Issue. 5, p. 391.
The use of the mild-slope approximation, which is invoked to simplify the problem of linear water wave diffraction-refraction by bed undulations, is reassessed by using a variational method. It is found that smooth approximations to the free surface elevation obtained by using the long-standing mild-slope equation are not consistent with the continuity of mass flow at locations where the bed slope is discontinuous. The use of interfacial jump conditions at such locations significantly improves the accuracy of approximations generated by the mild-slope equation and by the recently derived modified mild-slope equation. The variational principle is also used to produce a generalization of these equations and of the associated jump condition. Numerical results are presented to illustrate the main points of the theory.
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