{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,5]],"date-time":"2026-10-05T09:24:19Z","timestamp":1791192259017,"version":"4.1.0"},"reference-count":52,"publisher":"The Royal Society","issue":"2134","license":[{"start":{"date-parts":[[2011,6,15]],"date-time":"2011-06-15T00:00:00Z","timestamp":1308096000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/royalsociety.org\/journals\/ethics-policies\/data-sharing-mining\/"}],"content-domain":{"domain":["royalsocietypublishing.org"],"crossmark-restriction":true},"short-container-title":["Proc. R. Soc. A."],"published-print":{"date-parts":[[2011,10,8]]},"abstract":"<jats:p>\n                    The \u2018New Year Wave\u2019 was recorded at the Draupner platform in the North Sea and is a rare high-quality measurement of a \u2018freak\u2019 or \u2018rogue\u2019 wave. The wave has been the subject of much interest and numerous studies. Despite this, the event has still not been satisfactorily explained. One piece of information that was not directly measured at the platform, but which is vital to understanding the nonlinear dynamics is the wave's directional spreading. This paper investigates the directionality of the Draupner wave and concludes it might have resulted from two wave-groups crossing, whose mean wave directions were separated by about 90\n                    <jats:sup>\u00b0<\/jats:sup>\n                    or more. This result has been deduced from a set-up of the low-frequency second-order difference waves under the giant wave, which can be explained only if two wave systems are propagating at such an angle. To check whether second-order theory is satisfactory for such a highly nonlinear event, we have run numerical simulations using a fully nonlinear potential flow solver, which confirm the conclusion deduced from the second-order theory. This is backed up by a hindcast from European Centre for Medium-Range Weather Forecasts that shows swell waves propagating at approximately 80\n                    <jats:sup>\u00b0<\/jats:sup>\n                    to the wind sea. Other evidence that supports our conclusion are the measured forces on the structure, the magnitude of the second-order sum waves and some other instances of freak waves occurring in crossing sea states.\n                  <\/jats:p>","DOI":"10.1098\/rspa.2011.0049","type":"journal-article","created":{"date-parts":[[2011,6,15]],"date-time":"2011-06-15T05:24:39Z","timestamp":1308115479000},"page":"3004-3021","update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":67,"title":["Did the Draupner wave occur in a crossing sea?"],"prefix":"10.1098","volume":"467","author":[{"given":"T. A. A.","family":"Adcock","sequence":"first","affiliation":[{"name":"Department of Engineering Science, University of Oxford, Oxford, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P. H.","family":"Taylor","sequence":"additional","affiliation":[{"name":"Department of Engineering Science, University of Oxford, Oxford, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"S.","family":"Yan","sequence":"additional","affiliation":[{"name":"School of Engineering and Mathematical Sciences, City University, London, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Q. W.","family":"Ma","sequence":"additional","affiliation":[{"name":"School of Engineering and Mathematical Sciences, City University, London, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"P. A. E. M.","family":"Janssen","sequence":"additional","affiliation":[{"name":"European Centre for Medium-Range Weather Forecasts, Reading, UK"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"175","published-online":{"date-parts":[[2011,6,15]]},"reference":[{"key":"e_1_3_2_2_1","unstructured":"Adcock T. A. A.. 2009 Aspects of wave dynamics and statistics on the open ocean. DPhil thesis Oxford UK:University of Oxford."},{"key":"e_1_3_2_3_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0031"},{"key":"e_1_3_2_4_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0224"},{"key":"e_1_3_2_5_1","doi-asserted-by":"publisher","DOI":"10.1115\/OMAE2010-20993"},{"key":"e_1_3_2_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/0141-1187(83)90067-6"},{"key":"e_1_3_2_7_1","article-title":"Second-order crest statistics of realistic sea states","author":"Christou M.","year":"2009","journal-title":"Proc. of the 11th Int. Workshop on Wave Hindcasting and Forecasting, Halifax, Canada, 18\u201323 October 2009"},{"key":"e_1_3_2_8_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.3160533"},{"key":"e_1_3_2_9_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0141-1187(99)00008-5"},{"key":"e_1_3_2_10_1","first-page":"1211","volume-title":"Proc. Int. Symp. on Hydrodynamics in Ocean Engineering","author":"Dean R. G.","year":"1981"},{"key":"e_1_3_2_11_1","volume-title":"Proc. of the 14th Winter Workshop \u2018Aha Huliko\u2019, 25\u201328 January 2005","author":"Donelan M. A.","year":"2005"},{"key":"e_1_3_2_12_1","doi-asserted-by":"publisher","DOI":"10.1146\/annurev.fluid.40.111406.102203"},{"key":"e_1_3_2_13_1","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0485(1998)028<0495:OOTDSO>2.0.CO;2"},{"key":"e_1_3_2_14_1","first-page":"57499","article-title":"Wavelet analysis of an extreme wave in a model basin","author":"Ewans K. C.","year":"2008","journal-title":"Proc. 27 Int. Conf. Offshore Mech and Arctic Engineering, Estoril, Portugal, 15\u201320 June 2008"},{"key":"e_1_3_2_15_1","first-page":"53","article-title":"Freak waves at campos Basin, Brazil","volume":"22","author":"Ferreira de Pinho U.","year":"2004","journal-title":"Geofizica"},{"key":"e_1_3_2_16_1","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0485(2000)030<1931:WCDOAS>2.0.CO;2"},{"key":"e_1_3_2_17_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apor.2005.11.009"},{"key":"e_1_3_2_18_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112007006507"},{"key":"e_1_3_2_19_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.oceaneng.2003.10.014"},{"key":"e_1_3_2_20_1","doi-asserted-by":"publisher","DOI":"10.1201\/9781439833483.ch11"},{"key":"e_1_3_2_21_1","article-title":"A possible freak wave event measured at the Draupner jacket January 1 1995","author":"Haver S.","year":"2004","journal-title":"Rogue waves Workshop, Brest."},{"key":"e_1_3_2_22_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112009990607"},{"key":"e_1_3_2_23_1","doi-asserted-by":"publisher","DOI":"10.1175\/1520-0485(2003)33<863:NFIAFW>2.0.CO;2"},{"key":"e_1_3_2_24_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112009008131"},{"key":"e_1_3_2_25_1","doi-asserted-by":"publisher","DOI":"10.1175\/JPO3128.1"},{"key":"e_1_3_2_26_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112005006841"},{"key":"e_1_3_2_27_1","article-title":"Performance of third generation wave models in extreme hurricanes","author":"Jensen R. E.","year":"2006","journal-title":"9th Int. Wind and Wave Workshop, 25\u201329 September, Victoria, BC"},{"key":"e_1_3_2_28_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2000.0702"},{"key":"e_1_3_2_29_1","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2010.0280"},{"key":"e_1_3_2_30_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.euromechflu.2003.09.002"},{"key":"e_1_3_2_31_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511628955"},{"key":"e_1_3_2_32_1","first-page":"97","article-title":"Wavelet and Local Directional Analysis of Ocean Waves","volume":"16","author":"Krogstad H. E.","year":"2006","journal-title":"Int. J. Offshore Polar Eng."},{"key":"e_1_3_2_33_1","first-page":"57","article-title":"A chronology of freak wave encounters","volume":"24","author":"Liu P. C.","year":"2007","journal-title":"Geofizika"},{"key":"e_1_3_2_34_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.06.014"},{"key":"e_1_3_2_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2005.06.014"},{"key":"e_1_3_2_36_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112006009815"},{"key":"e_1_3_2_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.euromechflu.2006.01.002"},{"key":"e_1_3_2_38_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.96.014503"},{"key":"e_1_3_2_39_1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.102.114502"},{"key":"e_1_3_2_40_1","article-title":"Rogue wave slams Gloucester dragger","author":"Prybot P. K.","year":"2007","journal-title":"Gloucester Daily Times"},{"key":"e_1_3_2_41_1","doi-asserted-by":"publisher","DOI":"10.1115\/1.2918126"},{"key":"e_1_3_2_42_1","doi-asserted-by":"publisher","DOI":"10.1134\/S0021364006240039"},{"key":"e_1_3_2_43_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apor.2006.03.003"},{"key":"e_1_3_2_44_1","doi-asserted-by":"publisher","DOI":"10.1175\/2007JPO3634.1"},{"key":"e_1_3_2_45_1","doi-asserted-by":"publisher","DOI":"10.1017\/S002211201000385X"},{"key":"e_1_3_2_46_1","first-page":"64","article-title":"A new model for the kinematics of large ocean waves\u2014application as a design wave","volume":"3","author":"Tromans P. S.","year":"1991","journal-title":"Proc. 1st Int. Conf. Offshore Mech. and Polar Engng (ISOPE), Edinburgh, UK, 11\u201316 August 1991"},{"key":"e_1_3_2_47_1","first-page":"265","article-title":"Simulating the spatial evolution of a measured time series of a freak wave","author":"Trulsen K.","year":"2001","journal-title":"Proc. of Rogue Waves 2000, 29\u201330 November 2000"},{"key":"e_1_3_2_48_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apor.2005.02.001"},{"key":"e_1_3_2_49_1","doi-asserted-by":"publisher","DOI":"10.1175\/2009JPO4147.1"},{"key":"e_1_3_2_50_1","first-page":"168","article-title":"Nonlinear simulations of 3D freak waves using a fast numerical method","volume":"19","author":"Yan S.","year":"2009","journal-title":"Int. J. Offshore Polar Eng."},{"key":"e_1_3_2_51_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.euromechflu.2009.08.001"},{"key":"e_1_3_2_52_1","doi-asserted-by":"publisher","DOI":"10.1002\/fld.2100"},{"key":"e_1_3_2_53_1","doi-asserted-by":"publisher","DOI":"10.1115\/OMAE2010-20455"}],"container-title":["Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rspa.2011.0049","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/full-xml\/10.1098\/rspa.2011.0049","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/royalsocietypublishing.org\/doi\/pdf\/10.1098\/rspa.2011.0049","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,12]],"date-time":"2026-05-12T21:24:16Z","timestamp":1778621056000},"score":1,"resource":{"primary":{"URL":"http:\/\/royalsocietypublishing.org\/rspa\/article\/467\/2134\/3004-3021\/83260"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,15]]},"references-count":52,"journal-issue":{"issue":"2134","published-print":{"date-parts":[[2011,10,8]]}},"alternative-id":["10.1098\/rspa.2011.0049"],"URL":"https:\/\/doi.org\/10.1098\/rspa.2011.0049","relation":{},"ISSN":["1364-5021","1471-2946"],"issn-type":[{"value":"1364-5021","type":"print"},{"value":"1471-2946","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6,15]]},"assertion":[{"value":"2011-01-18","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-05-18","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2011-06-15","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}