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The interaction of periodic surface gravity waves with slowly varying water currents
Includes bibliography.
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| Main Author: | |
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| Other Authors: | |
| Format: | Thesis |
| Language: | English |
| Published: |
Department of Oceanography
2014
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| _version_ | 1867613236130480128 |
|---|---|
| access_status_str | Open Access |
| author | Bleach, Gordon Phillip |
| author2 | Brundrit, Geoff |
| author_browse | Bleach, Gordon Phillip Brundrit, Geoff |
| author_facet | Brundrit, Geoff Bleach, Gordon Phillip |
| author_sort | Bleach, Gordon Phillip |
| collection | Thesis |
| description | Includes bibliography. |
| format | Thesis |
| id | oai:open.uct.ac.za:11427/9972 |
| institution | University of Cape Town (South Africa) |
| language | eng |
| last_indexed | 2026-06-10T12:32:56.154Z |
| license_str | Not specified — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UCTD — University of Cape Town Open Access Repository |
| publishDate | 2014 |
| publishDateRange | 2014 |
| publishDateSort | 2014 |
| publisher | Department of Oceanography |
| publisherStr | Department of Oceanography |
| record_format | dspace |
| source_str | UCTD — University of Cape Town Open Access Repository |
| spelling | oai:open.uct.ac.za:11427/9972 The interaction of periodic surface gravity waves with slowly varying water currents Bleach, Gordon Phillip Brundrit, Geoff Applied Mathematics Includes bibliography. 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. 2014-12-11T21:02:32Z 2014-12-11T21:02:32Z 1982 Master Thesis Masters MSc http://hdl.handle.net/11427/9972 eng application/pdf Department of Oceanography Faculty of Science University of Cape Town |
| spellingShingle | Applied Mathematics Bleach, Gordon Phillip The interaction of periodic surface gravity waves with slowly varying water currents |
| thesis_degree_str | Master's |
| title | The interaction of periodic surface gravity waves with slowly varying water currents |
| title_full | The interaction of periodic surface gravity waves with slowly varying water currents |
| title_fullStr | The interaction of periodic surface gravity waves with slowly varying water currents |
| title_full_unstemmed | The interaction of periodic surface gravity waves with slowly varying water currents |
| title_short | The interaction of periodic surface gravity waves with slowly varying water currents |
| title_sort | interaction of periodic surface gravity waves with slowly varying water currents |
| topic | Applied Mathematics |
| url | http://hdl.handle.net/11427/9972 |
| work_keys_str_mv | AT bleachgordonphillip theinteractionofperiodicsurfacegravitywaveswithslowlyvaryingwatercurrents AT bleachgordonphillip interactionofperiodicsurfacegravitywaveswithslowlyvaryingwatercurrents |