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Analytical solution for long - wave reflection by a general breakwater or trench with curvilinear slopes / Huan-Wen Liu in Journal of engineering mechanics, Vol. 139 N° 2 (Février 2013) 

Public ISBD [article]  in Journal of engineering mechanics > Vol. 139 N° 2 (Février 2013) . - pp.229–245. Titre : Analytical solution for long - wave reflection by a general breakwater or trench with curvilinear slopes Type de document : texte imprimé Auteurs : Huan-Wen Liu, Auteur ; Jiong-Xing Luo, Auteur ; Pengzhi Lin, Auteur Année de publication : 2013 Article en page(s) : pp.229–245. Note générale : Applied mechanics Langues : Anglais (eng) Mots-clés : Long-wave  equation  General  breakwater  or  trench  Curvilinear  slope  Reflection  coefficient  Closed-form  solution  Series  solution Résumé : In the first part of this paper, an exact analytical solution in closed form for linear long-wave reflection by a submerged idealized breakwater or trench with various curvilinear slopes is given. The solution obtained finds almost all previous long-wave analytical solutions for wave reflection by idealized bathymetries to be its special cases, including the wave reflection by an infinite step, a continental shelf with a parabolic slope, a continental shelf with a linear slope, a rectangular obstacle, an obstacle of general trapezoidal shape with linear slopes, and a trench of general trapezoidal shape with linear slopes. In the second part, an exact analytical solution in the form of a Taylor series for linear long-wave reflection by a submerged quasi-idealized breakwater or trench is also constructed. It is shown by convergence analysis that the series solution converges in the entire physical domain. Based on the present analytical solutions, the reflection coefficients for long waves reflected by various breakwaters are calculated and the influence of the breakwater dimensions in the reflection effect is investigated. It is always found that the total reflection defined by the area under the reflection coefficient curve increases when the front and back slopes become steep. It is also found that the phenomenon of zero reflection for a symmetrical rectangular breakwater still remains for a general breakwater with curvilinear slopes as long as the bathymetry is symmetrical about the breakwater. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000483 [article] Analytical solution for long - wave reflection by a general breakwater or trench with curvilinear slopes [texte imprimé] / Huan-Wen Liu, Auteur ; Jiong-Xing Luo, Auteur ; Pengzhi Lin, Auteur . - 2013 . - pp.229–245. Applied mechanics Langues : Anglais (eng) in Journal of engineering mechanics > Vol. 139 N° 2 (Février 2013) . - pp.229–245. Mots-clés : Long-wave  equation  General  breakwater  or  trench  Curvilinear  slope  Reflection  coefficient  Closed-form  solution  Series  solution Résumé : In the first part of this paper, an exact analytical solution in closed form for linear long-wave reflection by a submerged idealized breakwater or trench with various curvilinear slopes is given. The solution obtained finds almost all previous long-wave analytical solutions for wave reflection by idealized bathymetries to be its special cases, including the wave reflection by an infinite step, a continental shelf with a parabolic slope, a continental shelf with a linear slope, a rectangular obstacle, an obstacle of general trapezoidal shape with linear slopes, and a trench of general trapezoidal shape with linear slopes. In the second part, an exact analytical solution in the form of a Taylor series for linear long-wave reflection by a submerged quasi-idealized breakwater or trench is also constructed. It is shown by convergence analysis that the series solution converges in the entire physical domain. Based on the present analytical solutions, the reflection coefficients for long waves reflected by various breakwaters are calculated and the influence of the breakwater dimensions in the reflection effect is investigated. It is always found that the total reflection defined by the area under the reflection coefficient curve increases when the front and back slopes become steep. It is also found that the phenomenon of zero reflection for a symmetrical rectangular breakwater still remains for a general breakwater with curvilinear slopes as long as the bathymetry is symmetrical about the breakwater. ISSN : 0733-9399 En ligne : http://ascelibrary.org/doi/abs/10.1061/%28ASCE%29EM.1943-7889.0000483