Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation
Recently, the Whitham and capillary Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions for both and study their stability. We present plots of a re...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-03-01
|
| Series: | Fluids |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2311-5521/4/1/58 |
| _version_ | 1818428469131870208 |
|---|---|
| author | John D. Carter Morgan Rozman |
| author_facet | John D. Carter Morgan Rozman |
| author_sort | John D. Carter |
| collection | DOAJ |
| description | Recently, the Whitham and capillary Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions for both and study their stability. We present plots of a representative sampling of solutions for a range of wavelengths, wave speeds, wave heights, and surface tension values. Finally, we discuss the role these parameters play in the stability of these solutions. |
| first_indexed | 2024-12-14T15:02:07Z |
| format | Article |
| id | doaj.art-c4e2b18b363942c7b656dfe797ff3d74 |
| institution | Directory Open Access Journal |
| issn | 2311-5521 |
| language | English |
| last_indexed | 2024-12-14T15:02:07Z |
| publishDate | 2019-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fluids |
| spelling | doaj.art-c4e2b18b363942c7b656dfe797ff3d742022-12-21T22:56:48ZengMDPI AGFluids2311-55212019-03-01415810.3390/fluids4010058fluids4010058Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham EquationJohn D. Carter0Morgan Rozman1Mathematics Department, Seattle University, Seattle, WA 98122, USAMathematics Department, Seattle University, Seattle, WA 98122, USARecently, the Whitham and capillary Whitham equations were shown to accurately model the evolution of surface waves on shallow water. In order to gain a deeper understanding of these equations, we compute periodic, traveling-wave solutions for both and study their stability. We present plots of a representative sampling of solutions for a range of wavelengths, wave speeds, wave heights, and surface tension values. Finally, we discuss the role these parameters play in the stability of these solutions.https://www.mdpi.com/2311-5521/4/1/58Whitham equationfully-dispersivesurface tensiontraveling-wave solutionsstability |
| spellingShingle | John D. Carter Morgan Rozman Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation Fluids Whitham equation fully-dispersive surface tension traveling-wave solutions stability |
| title | Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation |
| title_full | Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation |
| title_fullStr | Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation |
| title_full_unstemmed | Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation |
| title_short | Stability of Periodic, Traveling-Wave Solutions to the Capillary Whitham Equation |
| title_sort | stability of periodic traveling wave solutions to the capillary whitham equation |
| topic | Whitham equation fully-dispersive surface tension traveling-wave solutions stability |
| url | https://www.mdpi.com/2311-5521/4/1/58 |
| work_keys_str_mv | AT johndcarter stabilityofperiodictravelingwavesolutionstothecapillarywhithamequation AT morganrozman stabilityofperiodictravelingwavesolutionstothecapillarywhithamequation |