Trapped Solitary Waves in a Periodic External Force: A Numerical Investigation Using the Whitham Equation and the Sponge Layer Method
This paper concerns the interaction between solitary waves on the surface of an ideal fluid and a localized external force, which models a moving disturbance on the free surface or an obstacle moving at the bottom of a channel. Previous works have investigated this interaction under the assumption t...
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| Format: | Article |
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MDPI AG
2023-08-01
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| Series: | Fluids |
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| Online Access: | https://www.mdpi.com/2311-5521/8/8/223 |
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| author | Marcelo V. Flamarion Roberto Ribeiro-Jr Diogo L. S. S. Vianna Alex M. Sato |
| author_facet | Marcelo V. Flamarion Roberto Ribeiro-Jr Diogo L. S. S. Vianna Alex M. Sato |
| author_sort | Marcelo V. Flamarion |
| collection | DOAJ |
| description | This paper concerns the interaction between solitary waves on the surface of an ideal fluid and a localized external force, which models a moving disturbance on the free surface or an obstacle moving at the bottom of a channel. Previous works have investigated this interaction under the assumption that the external force moves with variable speed and constant acceleration. However, in this paper we adopt a different approach and consider the scenario in which the external force moves with variable speed and non-constant acceleration. Using the Whitham equation framework, we investigate numerically trapped waves excited by a periodic external force. Our experiments reveal regimes in which solitary waves are spontaneously generated and trapped for large times at the external force. In addition, we compare the results predicted by the Whitham equation with those of the Korteweg–de Vries equation. |
| first_indexed | 2024-03-10T23:57:16Z |
| format | Article |
| id | doaj.art-65fe2481896d4aecb159fb099a1c7c4c |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-03-10T23:57:16Z |
| publishDate | 2023-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-65fe2481896d4aecb159fb099a1c7c4c2023-11-19T01:04:38ZengMDPI AGFluids2311-55212023-08-018822310.3390/fluids8080223Trapped Solitary Waves in a Periodic External Force: A Numerical Investigation Using the Whitham Equation and the Sponge Layer MethodMarcelo V. Flamarion0Roberto Ribeiro-Jr1Diogo L. S. S. Vianna2Alex M. Sato3Unidade Acadêmica do Cabo de Santo Agostinho, UFRPE/Rural Federal University of Pernambuco, BR 101 Sul, Cabo de Santo Agostinho 54503-900, BrazilDepartament of Mathematics, UFPR/Federal University of Paraná, Centro Politécnico, Jardim das Américas, Curitiba 81531-980, BrazilDepartament of Mathematics, UFPR/Federal University of Paraná, Centro Politécnico, Jardim das Américas, Curitiba 81531-980, BrazilDepartament of Mathematics, UFPR/Federal University of Paraná, Centro Politécnico, Jardim das Américas, Curitiba 81531-980, BrazilThis paper concerns the interaction between solitary waves on the surface of an ideal fluid and a localized external force, which models a moving disturbance on the free surface or an obstacle moving at the bottom of a channel. Previous works have investigated this interaction under the assumption that the external force moves with variable speed and constant acceleration. However, in this paper we adopt a different approach and consider the scenario in which the external force moves with variable speed and non-constant acceleration. Using the Whitham equation framework, we investigate numerically trapped waves excited by a periodic external force. Our experiments reveal regimes in which solitary waves are spontaneously generated and trapped for large times at the external force. In addition, we compare the results predicted by the Whitham equation with those of the Korteweg–de Vries equation.https://www.mdpi.com/2311-5521/8/8/223Whitham equationsponge layertrapped wavesnumerical methodperiodic external force |
| spellingShingle | Marcelo V. Flamarion Roberto Ribeiro-Jr Diogo L. S. S. Vianna Alex M. Sato Trapped Solitary Waves in a Periodic External Force: A Numerical Investigation Using the Whitham Equation and the Sponge Layer Method Fluids Whitham equation sponge layer trapped waves numerical method periodic external force |
| title | Trapped Solitary Waves in a Periodic External Force: A Numerical Investigation Using the Whitham Equation and the Sponge Layer Method |
| title_full | Trapped Solitary Waves in a Periodic External Force: A Numerical Investigation Using the Whitham Equation and the Sponge Layer Method |
| title_fullStr | Trapped Solitary Waves in a Periodic External Force: A Numerical Investigation Using the Whitham Equation and the Sponge Layer Method |
| title_full_unstemmed | Trapped Solitary Waves in a Periodic External Force: A Numerical Investigation Using the Whitham Equation and the Sponge Layer Method |
| title_short | Trapped Solitary Waves in a Periodic External Force: A Numerical Investigation Using the Whitham Equation and the Sponge Layer Method |
| title_sort | trapped solitary waves in a periodic external force a numerical investigation using the whitham equation and the sponge layer method |
| topic | Whitham equation sponge layer trapped waves numerical method periodic external force |
| url | https://www.mdpi.com/2311-5521/8/8/223 |
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