caa a22 4500 469065788 CHVBK 20180323132908.0 cr unu---uuuuu 170328e19920301xx s 000 0 eng 10.1007/BF02728494 doi (NATIONALLICENCE)springer-10.1007/BF02728494 The effect of a fixed barrier on an incident progressive wave in shallow water [Elektronische Daten] [M. Abou-Dina, M. Helal] Summary: The effect of a fixed barrier on the propagation of an incident wave inside an ideal fluid is investigated within the frame of the shallow-water theory in two dimensions. The fluid is supposed to occupy an infinite channel of constant depth. Further, the horizontal extent of the barrier is assumed to be small. An asymptotic double series expansion for the solution is used. This procedure enables us to obtain analytic expressions for the local perturbations. The results of the first-order approximation indicate that no reflections exist. The second-order approximation of the solution is found to be the superposition of a progressive wave and local perturbations. For approximations of order higher than two, a secular term which increases monotonically with time appears in the expressions for the progressive wave. This unacceptable result is due to certain aspects in the mathematical procedure used. For this reason, the procedure is modified by using a suitable transformation of variables which reduces the determination of the transmitted wave to the solution of the K.d.V. equation. As an illustration, the special case of the incident uniform flow is considered and the stream lines of the resulting flow are drawn. Società Italiana di Fisica, 1992 PACS 03.40.Ge Fluid dynamics nationallicence general mathematical aspects nationallicence PACS 47.35.i Hydrodynamics waves nationallicence Abou-Dina M. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt aut Helal M. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt aut Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/3(1992-03-01), 331-344 107:3<331 1992 107 40764 https://doi.org/10.1007/BF02728494 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02728494 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Abou-Dina M. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt aut NATIONALLICENCE 700 1- Helal M. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt aut NATIONALLICENCE 773 0- Il Nuovo Cimento B (1971-1996) Società Italiana di Fisica 107/3(1992-03-01), 331-344 107:3<331 1992 107 40764 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer