Modelling intermediate internal waves with currents and variable bottom
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918082571665408 |
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| author | Ivanov, Rossen Ivanova, Lyudmila |
| author_facet | Ivanov, Rossen Ivanova, Lyudmila |
| contents | A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that the upper layer is considerably deeper with a lower density than the lower layer. The fluid dynamics is presented in Hamiltonian form with appropriate Dirichlet-Neumann operators for the two fluid domains, and the depth-dependent current is taken into account. The well known integrable Intermediate Long Wave Equation (ILWE) is derived as an asymptotic internal waves model in the case of flat bottom. For a non-flat bottom the ILWE is with variable coefficients. Two limits of the ILWE lead to the integrable Benjamin-Ono and Korteweg-de Vries equations. Higher-order ILWE is obtained as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_10123 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Modelling intermediate internal waves with currents and variable bottom Ivanov, Rossen Ivanova, Lyudmila Pattern Formation and Solitons Fluid Dynamics 37K10, 76B55, 35Q51 A model for internal interfacial waves between two layers of fluid in the presence of current and variable bottom is studied in the flat-surface approximation. Fluids are assumed to be incompressible and inviscid. Another assumption is that the upper layer is considerably deeper with a lower density than the lower layer. The fluid dynamics is presented in Hamiltonian form with appropriate Dirichlet-Neumann operators for the two fluid domains, and the depth-dependent current is taken into account. The well known integrable Intermediate Long Wave Equation (ILWE) is derived as an asymptotic internal waves model in the case of flat bottom. For a non-flat bottom the ILWE is with variable coefficients. Two limits of the ILWE lead to the integrable Benjamin-Ono and Korteweg-de Vries equations. Higher-order ILWE is obtained as well. |
| title | Modelling intermediate internal waves with currents and variable bottom |
| topic | Pattern Formation and Solitons Fluid Dynamics 37K10, 76B55, 35Q51 |
| url | https://arxiv.org/abs/2506.10123 |