{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T14:03:25Z","timestamp":1751637805818},"reference-count":29,"publisher":"Hindawi Limited","license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>We obtain asymptotic formulas for the reflection\/transmission coefficients of linear long water waves, propagating in a harbor composed of a tapered and slender region connected to uniform inlet and outlet regions. The region with variable character obeys a power-law. The governing equations are presented in dimensionless form. The reflection\/transmission coefficients are obtained for the limit of the parameter<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:msub><mml:mrow><mml:mi>\u03ba<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msub><mml:mo>\u226a<\/mml:mo><mml:mn>1<\/mml:mn><\/mml:math>, which corresponds to a wavelength shorter than the characteristic horizontal length of the harbor. The asymptotic formulas consider those cases when the geometry of the harbor can be variable in width and depth: linear or parabolic among other transitions or a combination of these geometries. For harbors with nonlinear transitions, the parabolic geometry is less reflective than the other cases. The reflection coefficient for linear transitions just presents an oscillatory behavior. We can infer that the deducted formulas provide as first approximation a practical reference to the analysis of wave reflection\/transmission in harbors.<\/jats:p>","DOI":"10.1155\/2015\/184147","type":"journal-article","created":{"date-parts":[[2015,7,27]],"date-time":"2015-07-27T21:02:08Z","timestamp":1438030928000},"page":"1-10","source":"Crossref","is-referenced-by-count":3,"title":["Asymptotic Formulas for the Reflection\/Transmission of Long Water Waves Propagating in a Tapered and Slender Harbor"],"prefix":"10.1155","volume":"2015","author":[{"given":"Eric-Gustavo","family":"Bautista","sequence":"first","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional, SEPI ESIME Azcapotzalco, Avenida de las Granjas No. 682, Colonia Santa Catarina, Delegaci\u00f3n Azcapotzalco, 02250 M\u00e9xico, DF, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Federico","family":"M\u00e9ndez","sequence":"additional","affiliation":[{"name":"Departamento de Termofluidos, Facultad de Ingenier\u00eda, UNAM, 04510 M\u00e9xico, DF, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oscar","family":"Bautista","sequence":"additional","affiliation":[{"name":"Instituto Polit\u00e9cnico Nacional, SEPI ESIME Azcapotzalco, Avenida de las Granjas No. 682, Colonia Santa Catarina, Delegaci\u00f3n Azcapotzalco, 02250 M\u00e9xico, DF, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"98","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/S0141-1187(00)00013-4"},{"key":"2","year":"1992"},{"key":"3","year":"2009"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1016\/j.pocean.2006.04.002"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1016\/j.apor.2005.11.010"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.coastaleng.2007.02.002"},{"key":"7","volume":"23","year":"2005"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1016\/j.coastaleng.2013.05.004"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112092001186"},{"key":"11","year":"1932"},{"key":"12","doi-asserted-by":"crossref","first-page":"106","DOI":"10.1017\/S0305004100033235","volume":"54","year":"1958","journal-title":"Mathematical Proceedings of the Cambridge Philosophical Society"},{"key":"13","year":"1979"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.oceaneng.2005.11.017"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.oceaneng.2008.04.001"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.oceaneng.2012.05.014"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1016\/j.coastaleng.2003.08.002"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1016\/j.oceaneng.2014.03.027"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)0733-9399(2005)131:8(822)"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1061\/(asce)em.1943-7889.0000293"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1061\/(ASCE)EM.1943-7889.0000483"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1007\/bf01535691"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1016\/j.apor.2011.03.002"},{"key":"24","first-page":"1416","volume":"7","year":"2013","journal-title":"World Academy of Science, Engineering and Technology"},{"key":"25","volume":"24","year":"2006"},{"key":"26","volume":"1","year":"1997"},{"key":"27","volume":"2","year":"1984"},{"key":"28","year":"1978"},{"issue":"1","key":"29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1061\/JWHEAU.0000351","volume":"90","year":"1964","journal-title":"Journal of the Waterways and Harbors Division"},{"key":"31","volume":"3","year":"1995"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/184147.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/184147.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/184147.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,5,19]],"date-time":"2022-05-19T05:25:19Z","timestamp":1652937919000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/184147\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":29,"alternative-id":["184147","184147"],"URL":"https:\/\/doi.org\/10.1155\/2015\/184147","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"value":"1110-757X","type":"print"},{"value":"1687-0042","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]}}}