A topological study of gravity waves generated by moving bodies using the method of steepest descents
The standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any s...
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| Format: | Journal article |
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Royal Society
2016
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| _version_ | 1826306242246606848 |
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| author | Trinh, P |
| author_facet | Trinh, P |
| author_sort | Trinh, P |
| collection | OXFORD |
| description | The standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of steady-state flows at low speeds. The approach is made possible through a reduction of the water-wave equations to a complex-valued integral equation that can be studied using the method of steepest descents. The main result is a theory that establishes a correspondence between different bluff-bodied free-surface flow configurations, with the topology of the Riemann surface formed by the steepest descent paths. Then, when a geometrical feature of the body is modified, a corresponding change to the Riemann surface is observed, and the resultant effects to the water waves can be derived. This visual procedure is demonstrated for the case of two-dimensional free-surface flow past a surface-piercing ship and over an angled step in a channel. |
| first_indexed | 2024-03-07T06:44:58Z |
| format | Journal article |
| id | oxford-uuid:fa919d95-3f08-4fd9-866c-07b8a2bbc6ac |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:44:58Z |
| publishDate | 2016 |
| publisher | Royal Society |
| record_format | dspace |
| spelling | oxford-uuid:fa919d95-3f08-4fd9-866c-07b8a2bbc6ac2022-03-27T13:06:50ZA topological study of gravity waves generated by moving bodies using the method of steepest descentsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:fa919d95-3f08-4fd9-866c-07b8a2bbc6acSymplectic Elements at OxfordRoyal Society2016Trinh, PThe standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of steady-state flows at low speeds. The approach is made possible through a reduction of the water-wave equations to a complex-valued integral equation that can be studied using the method of steepest descents. The main result is a theory that establishes a correspondence between different bluff-bodied free-surface flow configurations, with the topology of the Riemann surface formed by the steepest descent paths. Then, when a geometrical feature of the body is modified, a corresponding change to the Riemann surface is observed, and the resultant effects to the water waves can be derived. This visual procedure is demonstrated for the case of two-dimensional free-surface flow past a surface-piercing ship and over an angled step in a channel. |
| spellingShingle | Trinh, P A topological study of gravity waves generated by moving bodies using the method of steepest descents |
| title | A topological study of gravity waves generated by moving bodies using the method of steepest descents |
| title_full | A topological study of gravity waves generated by moving bodies using the method of steepest descents |
| title_fullStr | A topological study of gravity waves generated by moving bodies using the method of steepest descents |
| title_full_unstemmed | A topological study of gravity waves generated by moving bodies using the method of steepest descents |
| title_short | A topological study of gravity waves generated by moving bodies using the method of steepest descents |
| title_sort | topological study of gravity waves generated by moving bodies using the method of steepest descents |
| work_keys_str_mv | AT trinhp atopologicalstudyofgravitywavesgeneratedbymovingbodiesusingthemethodofsteepestdescents AT trinhp topologicalstudyofgravitywavesgeneratedbymovingbodiesusingthemethodofsteepestdescents |