Wave evolution within the Cubic Vortical Whitham equation
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929520156606464 |
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| author | Flamarion, Marcelo V. Pelinovsky, Efim |
| author_facet | Flamarion, Marcelo V. Pelinovsky, Efim |
| contents | In this work, we study the evolution of disturbances within the framework of the Cubic Vortical Whitham (CV-Whitham) equation, considering both positive and negative cubic nonlinearities. This equation plays important role for description of the wave processes in the presence of shear flows. We find well-formed breather-type structures arising from the evolution of depression disturbances with positive cubic nonlinearity. For elevation disturbances, the results are two-fold. When the cubic nonlinearity is negative, we show that the CV-Whitham equation and the Gardner equation are qualitatively similar, differing only by a small phase lag due to differences in the dispersion term. However, with positive cubic nonlinearity, the differences between the solutions become more pronounced, with the CV-Whitham equation producing sharper waves that suggest the onset of wave breaking. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_19424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Wave evolution within the Cubic Vortical Whitham equation Flamarion, Marcelo V. Pelinovsky, Efim Pattern Formation and Solitons Fluid Dynamics In this work, we study the evolution of disturbances within the framework of the Cubic Vortical Whitham (CV-Whitham) equation, considering both positive and negative cubic nonlinearities. This equation plays important role for description of the wave processes in the presence of shear flows. We find well-formed breather-type structures arising from the evolution of depression disturbances with positive cubic nonlinearity. For elevation disturbances, the results are two-fold. When the cubic nonlinearity is negative, we show that the CV-Whitham equation and the Gardner equation are qualitatively similar, differing only by a small phase lag due to differences in the dispersion term. However, with positive cubic nonlinearity, the differences between the solutions become more pronounced, with the CV-Whitham equation producing sharper waves that suggest the onset of wave breaking. |
| title | Wave evolution within the Cubic Vortical Whitham equation |
| topic | Pattern Formation and Solitons Fluid Dynamics |
| url | https://arxiv.org/abs/2409.19424 |