The interaction of periodic surface gravity waves with slowly varying water currents

 

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dc.contributor.advisor Brundrit, Geoff en_ZA
dc.contributor.author Bleach, Gordon Phillip en_ZA
dc.date.accessioned 2014-12-11T21:02:32Z
dc.date.available 2014-12-11T21:02:32Z
dc.date.issued 1982 en_ZA
dc.identifier.citation Bleach, G. 1982. The interaction of periodic surface gravity waves with slowly varying water currents. University of Cape Town. en_ZA
dc.identifier.uri http://hdl.handle.net/11427/9972
dc.description Includes bibliography. en_ZA
dc.description.abstract The governing equations for interactions between surface gravity wavetrains and slowly-varying water currents are derived and the incorporation of Vocoidal water wave theory into this framework is discussed. The emphasis throughout is on the derivation of the general form of the governing equations plus a detailed discussion of the qualitative physical behaviour implied by the equations. Particular solutions are usually given only where they serve to clarify the general method or some physical feature of the analysis. The thesis proper is introduced by a derivation of wave kinematics on still water. A review of the kinematics and dynamics of an inviscid and irrotational fluid follows. The wave and fluid properties are then combined via the definition of wave integral properties. A derivation of the Airy and Stokes O(a2) wave theories is given and used to illustrate a number of points. Water currents (following or opposing the waves) are introduced via their influence on the wave-kinematics. The wave/current dynamics are then presented in two ways: firstly using a wave energy approach and secondly by introducing the wave action concept. Wave action is more convenient because it is a conserved quantity unlike wave energy. The general equations for two dimensional wave/current interactions are derived and discussed. At this point three topics are reconsidered: group velocity, momentum density in wave motion and Lagrangian mean forms of averaging. The general equations for wave/current interaction are shown to be compatible with the Vocoidal water wave theory and applications of the theory to wave/current problems are discussed. en_ZA
dc.language.iso eng en_ZA
dc.subject.other Applied Mathematics en_ZA
dc.title The interaction of periodic surface gravity waves with slowly varying water currents en_ZA
dc.type Master Thesis
uct.type.publication Research en_ZA
uct.type.resource Thesis en_ZA
dc.publisher.institution University of Cape Town
dc.publisher.faculty Faculty of Science en_ZA
dc.publisher.department Department of Oceanography en_ZA
dc.type.qualificationlevel Masters
dc.type.qualificationname MSc en_ZA
uct.type.filetype Text
uct.type.filetype Image
dc.identifier.apacitation Bleach, G. P. (1982). <i>The interaction of periodic surface gravity waves with slowly varying water currents</i>. (Thesis). University of Cape Town ,Faculty of Science ,Department of Oceanography. Retrieved from http://hdl.handle.net/11427/9972 en_ZA
dc.identifier.chicagocitation Bleach, Gordon Phillip. <i>"The interaction of periodic surface gravity waves with slowly varying water currents."</i> Thesis., University of Cape Town ,Faculty of Science ,Department of Oceanography, 1982. http://hdl.handle.net/11427/9972 en_ZA
dc.identifier.vancouvercitation Bleach GP. The interaction of periodic surface gravity waves with slowly varying water currents. [Thesis]. University of Cape Town ,Faculty of Science ,Department of Oceanography, 1982 [cited yyyy month dd]. Available from: http://hdl.handle.net/11427/9972 en_ZA
dc.identifier.ris TY - Thesis / Dissertation AU - Bleach, Gordon Phillip AB - The governing equations for interactions between surface gravity wavetrains and slowly-varying water currents are derived and the incorporation of Vocoidal water wave theory into this framework is discussed. The emphasis throughout is on the derivation of the general form of the governing equations plus a detailed discussion of the qualitative physical behaviour implied by the equations. Particular solutions are usually given only where they serve to clarify the general method or some physical feature of the analysis. The thesis proper is introduced by a derivation of wave kinematics on still water. A review of the kinematics and dynamics of an inviscid and irrotational fluid follows. The wave and fluid properties are then combined via the definition of wave integral properties. A derivation of the Airy and Stokes O(a2) wave theories is given and used to illustrate a number of points. Water currents (following or opposing the waves) are introduced via their influence on the wave-kinematics. The wave/current dynamics are then presented in two ways: firstly using a wave energy approach and secondly by introducing the wave action concept. Wave action is more convenient because it is a conserved quantity unlike wave energy. The general equations for two dimensional wave/current interactions are derived and discussed. At this point three topics are reconsidered: group velocity, momentum density in wave motion and Lagrangian mean forms of averaging. The general equations for wave/current interaction are shown to be compatible with the Vocoidal water wave theory and applications of the theory to wave/current problems are discussed. DA - 1982 DB - OpenUCT DP - University of Cape Town LK - https://open.uct.ac.za PB - University of Cape Town PY - 1982 T1 - The interaction of periodic surface gravity waves with slowly varying water currents TI - The interaction of periodic surface gravity waves with slowly varying water currents UR - http://hdl.handle.net/11427/9972 ER - en_ZA


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