{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T19:31:46Z","timestamp":1787340706374,"version":"build-2736575974"},"reference-count":19,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"5","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Appl. Math."],"published-print":{"date-parts":[[2000,1]]},"abstract":"<jats:p>In this paper we use a multiple scales approach to derive an equation governing the modulational stability of Taylor vortices in a high Reynolds number flow through a curved channel of small gap. The evolution equation governing the two-dimensional modulation of Taylor vortices is found to be a modified Burgers equation with a new nonlinear term ($A_{T}+A^{2}A_{X}=\\pm A_{XX} $). When finite but small curvature effects are accounted for, this modified Burgers equation generalizes to $A_{T}+A^{2}A_{X}=\\pm A_{XX} + \\lambda A$. Numerical solutions of this equation show that a family of periodic traveling waves exists, with profiles becoming increasingly steeper as the length of the system is increased.<\/jats:p>","DOI":"10.1137\/s003613999731557x","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1543-1564","source":"Crossref","is-referenced-by-count":2,"title":["The Modulational Stability of Taylor Vortices in a Curved Channel"],"prefix":"10.1137","volume":"60","author":[{"given":"A. H.","family":"Dando","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"D. T.","family":"Papageorgiou","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P.","family":"Hall","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,27]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112091001507"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1959.0091"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112074001765"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.1928.0205"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112075000183"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112086000356"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160470304"},{"key":"R8","first-page":"1","volume":"2","author":"G\u00f6rtler H.","year":"1940","journal-title":"Nach. Ges. Wiss. G\u00f6ttingen, N. F."},{"key":"R9","doi-asserted-by":"crossref","unstructured":"J. Guckenheimer and P. Holmes,\n                      Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields\n                      , Springer\u2010Verlag, New York, 1983.","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112083000968"},{"key":"R11","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112089001801"},{"key":"R12","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112091000289"},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112083000968"},{"key":"R14","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139995285765"},{"key":"R15","volume-title":"B\u00e9nard cells and Taylor vortices","author":"Koschmieder E.","year":"1993"},{"key":"R16","doi-asserted-by":"crossref","unstructured":"D. T. Papageorgiou, G. C. Papanicolaou, and Y. S. Smyrlis,\n                      Modulational stability of periodic solutions of the Kuramoto\u2010Sivashinsky equation\n                      , in Singularities in Fluids, Plasmas and Optics, NATO ASI Series C, vol. 404, R. E. Caflisch and G. C. Papanicolaou, eds., 1992.","DOI":"10.1007\/978-94-011-2022-7_19"},{"key":"R17","unstructured":"Y. S. Smyrlis and D. T. Papageorgiou,\n                      Computational study of chaotic and ordered solutions of the Kuramoto\u2010Sivashinsky equation\n                      , in Advances in Multi\u2010Fluid Flows, Proceedings of the AMS\u2010IMS\u2010SIAM Joint Summer Research Conference on Multi\u2010Fluid Flows and Interfacial Instabilities, SIAM, Philadelphia, 1996."},{"key":"R18","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1923.0008"},{"key":"R19","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112094002685"}],"container-title":["SIAM Journal on Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/S003613999731557X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T18:44:53Z","timestamp":1787337893000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/S003613999731557X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,1]]},"references-count":19,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2000,1]]}},"alternative-id":["10.1137\/S003613999731557X"],"URL":"https:\/\/doi.org\/10.1137\/s003613999731557x","relation":{},"ISSN":["0036-1399","1095-712X"],"issn-type":[{"value":"0036-1399","type":"print"},{"value":"1095-712X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,1]]}}}