{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,19]],"date-time":"2025-11-19T14:49:08Z","timestamp":1763563748554},"reference-count":36,"publisher":"Cambridge University Press (CUP)","license":[{"start":{"date-parts":[[2010,7,6]],"date-time":"2010-07-06T00:00:00Z","timestamp":1278374400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Fluid Mech."],"published-print":{"date-parts":[[2010,9,25]]},"abstract":"<jats:p>Existence of edge waves travelling along three-dimensional periodic structures is considered within the linear water-wave theory. A condition ensuring the existence is derived by analysing the spectrum of a suitably defined trace operator. The sufficient condition is a simple inequality comparing a weighted volume integral, taken over the submerged part of an element in the infinite array of identical obstacles, to the area of the free surface pierced by the obstacle. Various examples are given, and the results are extended to edge waves along periodic coastlines and over a periodically varying ocean floor.<\/jats:p>","DOI":"10.1017\/s0022112010002429","type":"journal-article","created":{"date-parts":[[2010,7,6]],"date-time":"2010-07-06T04:38:47Z","timestamp":1278391127000},"page":"225-246","source":"Crossref","is-referenced-by-count":16,"title":["Existence of edge waves along three-dimensional periodic structures"],"prefix":"10.1017","volume":"659","author":[{"given":"SERGEY A.","family":"NAZAROV","sequence":"first","affiliation":[]},{"given":"JUHA H.","family":"VIDEMAN","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2010,7,6]]},"reference":[{"key":"S0022112010002429_ref34","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1952.0152"},{"key":"S0022112010002429_ref31","first-page":"1","volume-title":"16th Meeting of the British Association for the Advancement of Science","author":"Stokes","year":"1846"},{"key":"S0022112010002429_ref13","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546778"},{"key":"S0022112010002429_ref25","doi-asserted-by":"publisher","DOI":"10.7146\/math.scand.a-15129"},{"key":"S0022112010002429_ref2","doi-asserted-by":"publisher","DOI":"10.1137\/0153071"},{"key":"S0022112010002429_ref21","doi-asserted-by":"publisher","DOI":"10.1007\/978-0-387-85650-6_12"},{"key":"S0022112010002429_ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.crme.2009.06.029"},{"key":"S0022112010002429_ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.wavemoti.2007.04.009"},{"key":"S0022112010002429_ref1","doi-asserted-by":"crossref","DOI":"10.1007\/978-94-009-4586-9","volume-title":"Spectral Theory of Self-Adjoint Operators in Hilbert Space","author":"Birman","year":"1987"},{"key":"S0022112010002429_ref15","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112002002227"},{"key":"S0022112010002429_ref27","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112099004425"},{"key":"S0022112010002429_ref18","first-page":"53","article-title":"Concentration of trapped modes in problems of the linearized theory of water waves","volume":"199","author":"Nazarov","year":"2008","journal-title":"Mat. Sbornik"},{"key":"S0022112010002429_ref20","first-page":"1","article-title":"A simple method for finding trapped modes in problems of the linear theory of surface waves","volume":"429","author":"Nazarov","year":"2009","journal-title":"Dokl. Ross. Akad. Nauk."},{"key":"S0022112010002429_ref23","doi-asserted-by":"publisher","DOI":"10.1515\/9783110848915"},{"key":"S0022112010002429_ref35","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112087002702"},{"key":"S0022112010002429_ref17","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1998.0272"},{"key":"S0022112010002429_ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.wavemoti.2005.05.005"},{"key":"S0022112010002429_ref26","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0281"},{"key":"S0022112010002429_ref6","doi-asserted-by":"publisher","DOI":"10.1007\/BF00253152"},{"key":"S0022112010002429_ref5","doi-asserted-by":"publisher","DOI":"10.1093\/qjmam\/46.4.643"},{"key":"S0022112010002429_ref32","first-page":"175","article-title":"Waveguide, anomalous, and whispering properties of a periodic chain of obstacles","volume":"1","author":"Sukhinin","year":"1998","journal-title":"Sib. Zh. Ind. Mat."},{"key":"S0022112010002429_ref4","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112094000236"},{"key":"S0022112010002429_ref24","first-page":"56","article-title":"On the spectrum of the Steklov problem in a domain with a peak","volume":"1","author":"Nazarov","year":"2008","journal-title":"Vestnik St.-Petersburg Univ."},{"key":"S0022112010002429_ref30","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160110403"},{"key":"S0022112010002429_ref12","volume-title":"Fluid Mechanics","author":"Kundu","year":"2004"},{"key":"S0022112010002429_ref3","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112095003119"},{"key":"S0022112010002429_ref9","first-page":"771","article-title":"Elastic waves localized near periodic sets of flaws","volume":"368","author":"Kamotskii","year":"1999","journal-title":"Dokl. Ross. Akad. Nauk."},{"key":"S0022112010002429_ref11","first-page":"227","article-title":"Boundary value problems for elliptic equations in domains with conical or angular points","volume":"16","author":"Kondratiev","year":"1967","journal-title":"Trans. Moscow Math. Soc."},{"key":"S0022112010002429_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100028875"},{"key":"S0022112010002429_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4317-3"},{"key":"S0022112010002429_ref36","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1130-3"},{"key":"S0022112010002429_ref33","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100026700"},{"key":"S0022112010002429_ref29","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112001003676"},{"key":"S0022112010002429_ref22","first-page":"202","article-title":"Sufficient conditions for the existence of trapped modes in problems of the linear theory of surface waves","volume":"369","author":"Nazarov","year":"2009","journal-title":"Zap. Nauchn. Semin. St.-Petersburg Otdel. Mat. Inst. Steklov"},{"key":"S0022112010002429_ref7","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160030106"},{"key":"S0022112010002429_ref10","first-page":"138","article-title":"Exponentially decreasing solutions of the problem of diffraction by a rigid periodic boundary","volume":"73","author":"Kamotskii","year":"2003","journal-title":"Mat. Zametki"}],"container-title":["Journal of Fluid Mechanics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022112010002429","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,7]],"date-time":"2019-06-07T16:36:02Z","timestamp":1559925362000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022112010002429\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,6]]},"references-count":36,"alternative-id":["S0022112010002429"],"URL":"https:\/\/doi.org\/10.1017\/s0022112010002429","relation":{},"ISSN":["0022-1120","1469-7645"],"issn-type":[{"value":"0022-1120","type":"print"},{"value":"1469-7645","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,6]]}}}