{"id":{"repo_id":"cape-town","oai_identifier":"oai:open.uct.ac.za:11427/9972"},"canonical_url":"https://search.dev.ndltd.org/etd/cape-town/oai:open.uct.ac.za:11427/9972","repository":{"repo_id":"cape-town","name":"University of Cape Town","base_url":"https://open.uct.ac.za/oai/request"},"display":{"title":"The interaction of periodic surface gravity waves with slowly varying water currents","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Bleach, Gordon Phillip"],"institution":"Department of Oceanography","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Brundrit, Geoff"],"committee_chairs":[],"committee_members":[],"year":1982,"date_issued":"1982","date_published":"1982","updated_at":"2026-07-22T22:23:02Z","subjects":[],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11427/9972","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Brundrit, Geoff"]},{"key":"dc:creator","label":"Author","values":["Bleach, Gordon Phillip"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2014-12-11T21:02:32Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2014-12-11T21:02:32Z"]},{"key":"dc:date.issued","label":"Date","values":["1982"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Department of Oceanography"]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Cape Town"]},{"key":"dc:type","label":"Dc Type","values":["Master Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["Masters"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["MSc"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11427/9972"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Includes bibliography."]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:title","label":"Title","values":["The interaction of periodic surface gravity waves with slowly varying water currents"]}]}],"canonical_facts":{"dc:contributor.advisor":["Brundrit, Geoff"],"dc:creator":["Bleach, Gordon Phillip"],"dc:date.accessioned":["2014-12-11T21:02:32Z"],"dc:date.available":["2014-12-11T21:02:32Z"],"dc:date.issued":["1982"],"dc:description":["Includes bibliography."],"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."],"dc:identifier.uri":["http://hdl.handle.net/11427/9972"],"dc:language.iso":["eng"],"dc:publisher.department":["Department of Oceanography"],"dc:publisher.institution":["University of Cape Town"],"dc:title":["The interaction of periodic surface gravity waves with slowly varying water currents"],"dc:type":["Master Thesis"],"dc:type.qualificationlevel":["Masters"],"dc:type.qualificationname":["MSc"]},"updated_at":"2026-07-22T22:23:02Z"}