The Euler-type description of Lagrangian water waves
A new description of 2D continuous free-surface flows in Lagrangian coordinates is proposed. It is shown that the position of a fluid particle in such flows can be represented as a fixed point of a transformation in ℝ2. Components of a transformation function satisfy the linear Euler-type continuity...
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| Format: | Conference item |
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WITPress
2005
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| _version_ | 1797074506655727616 |
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| author | Buldakov, E Taylor, P Taylor, R |
| author_facet | Buldakov, E Taylor, P Taylor, R |
| author_sort | Buldakov, E |
| collection | OXFORD |
| description | A new description of 2D continuous free-surface flows in Lagrangian coordinates is proposed. It is shown that the position of a fluid particle in such flows can be represented as a fixed point of a transformation in ℝ2. Components of a transformation function satisfy the linear Euler-type continuity equation and can be expressed via a single function analogous to an Eulerian stream function. Fixed-point iterations lead to a simple recursive representation of a solution satisfying the Lagrangian continuity equation. Expanding the unknown function into a small-perturbation asymptotic expansion we obtain the complete asymptotic formulation of the problem in a fixed domain of Lagrangian labels. The method is then applied to a classical problem of a regular wave traveling in deep water, and the fifth order Lagrangian asymptotic solution is constructed. In contrast with early attempts of Lagrangian regular-wave expansions, the presented asymptotic solution is uniformly-valid at large times. © 2005 WIT Press. |
| first_indexed | 2024-03-06T23:37:10Z |
| format | Conference item |
| id | oxford-uuid:6e0ba5bf-e195-40f1-8f71-3f94ee7bc9dd |
| institution | University of Oxford |
| last_indexed | 2024-03-06T23:37:10Z |
| publishDate | 2005 |
| publisher | WITPress |
| record_format | dspace |
| spelling | oxford-uuid:6e0ba5bf-e195-40f1-8f71-3f94ee7bc9dd2022-03-26T19:21:51ZThe Euler-type description of Lagrangian water wavesConference itemhttp://purl.org/coar/resource_type/c_5794uuid:6e0ba5bf-e195-40f1-8f71-3f94ee7bc9ddSymplectic Elements at OxfordWITPress2005Buldakov, ETaylor, PTaylor, RA new description of 2D continuous free-surface flows in Lagrangian coordinates is proposed. It is shown that the position of a fluid particle in such flows can be represented as a fixed point of a transformation in ℝ2. Components of a transformation function satisfy the linear Euler-type continuity equation and can be expressed via a single function analogous to an Eulerian stream function. Fixed-point iterations lead to a simple recursive representation of a solution satisfying the Lagrangian continuity equation. Expanding the unknown function into a small-perturbation asymptotic expansion we obtain the complete asymptotic formulation of the problem in a fixed domain of Lagrangian labels. The method is then applied to a classical problem of a regular wave traveling in deep water, and the fifth order Lagrangian asymptotic solution is constructed. In contrast with early attempts of Lagrangian regular-wave expansions, the presented asymptotic solution is uniformly-valid at large times. © 2005 WIT Press. |
| spellingShingle | Buldakov, E Taylor, P Taylor, R The Euler-type description of Lagrangian water waves |
| title | The Euler-type description of Lagrangian water waves |
| title_full | The Euler-type description of Lagrangian water waves |
| title_fullStr | The Euler-type description of Lagrangian water waves |
| title_full_unstemmed | The Euler-type description of Lagrangian water waves |
| title_short | The Euler-type description of Lagrangian water waves |
| title_sort | euler type description of lagrangian water waves |
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