Two-dimensional Stokes flow with suction and small surface tension
In this article the complex variable theory of two-dimensional Stokes flow as developed by Richardson [22], and modified by Howison Richardson [16], is reviewed. The analysis of [16] is extended to a new solution driven by a point sink, which uses a cubic polynomial conformal mapping (with real coef...
| Main Authors: | , |
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| Format: | Journal article |
| Language: | English |
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1999
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| _version_ | 1797063883680120832 |
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| author | Cummings, L Howison, S |
| author_facet | Cummings, L Howison, S |
| author_sort | Cummings, L |
| collection | OXFORD |
| description | In this article the complex variable theory of two-dimensional Stokes flow as developed by Richardson [22], and modified by Howison Richardson [16], is reviewed. The analysis of [16] is extended to a new solution driven by a point sink, which uses a cubic polynomial conformal mapping (with real coefficients) from the unit disk onto the fluid domain. This solution is analysed in the limit of small surface tension. An apparent 'stability paradox' (where two equivalent flow geometries are found, one of which is 'stable' and the other unstable) is resolved by allowing the coefficients to take complex values. |
| first_indexed | 2024-03-06T21:06:20Z |
| format | Journal article |
| id | oxford-uuid:3c98a6bc-9aa8-466a-8f81-72cbed9e860b |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-06T21:06:20Z |
| publishDate | 1999 |
| record_format | dspace |
| spelling | oxford-uuid:3c98a6bc-9aa8-466a-8f81-72cbed9e860b2022-03-26T14:14:27ZTwo-dimensional Stokes flow with suction and small surface tensionJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:3c98a6bc-9aa8-466a-8f81-72cbed9e860bEnglishSymplectic Elements at Oxford1999Cummings, LHowison, SIn this article the complex variable theory of two-dimensional Stokes flow as developed by Richardson [22], and modified by Howison Richardson [16], is reviewed. The analysis of [16] is extended to a new solution driven by a point sink, which uses a cubic polynomial conformal mapping (with real coefficients) from the unit disk onto the fluid domain. This solution is analysed in the limit of small surface tension. An apparent 'stability paradox' (where two equivalent flow geometries are found, one of which is 'stable' and the other unstable) is resolved by allowing the coefficients to take complex values. |
| spellingShingle | Cummings, L Howison, S Two-dimensional Stokes flow with suction and small surface tension |
| title | Two-dimensional Stokes flow with suction and small surface tension |
| title_full | Two-dimensional Stokes flow with suction and small surface tension |
| title_fullStr | Two-dimensional Stokes flow with suction and small surface tension |
| title_full_unstemmed | Two-dimensional Stokes flow with suction and small surface tension |
| title_short | Two-dimensional Stokes flow with suction and small surface tension |
| title_sort | two dimensional stokes flow with suction and small surface tension |
| work_keys_str_mv | AT cummingsl twodimensionalstokesflowwithsuctionandsmallsurfacetension AT howisons twodimensionalstokesflowwithsuctionandsmallsurfacetension |