On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909621591998464 |
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| author | Shashikanth, Banavara N. |
| author_facet | Shashikanth, Banavara N. |
| contents | Motivated by the work of previous authors on vortex sheets and their applications, the intrinsic inviscid evolution equations of a closed vortex sheet in a plane, separating two piecewise constant density fluids, and their Hamiltonian form are investigated. The model has potential applications to problems involving the dynamics of interfaces of two immiscible fluids. A boundary Poisson bracket, which appears to be new and related to the KdV bracket, is obtained containing the curve-tangential derivative $\partial / \partial s$. Lagrangian invariants of the sheet motion by its self-induced velocity--the Cauchy principal value of the Biot-Savart integral--are also derived. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13462 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet Shashikanth, Banavara N. Fluid Dynamics Other Condensed Matter Mathematical Physics Pattern Formation and Solitons Motivated by the work of previous authors on vortex sheets and their applications, the intrinsic inviscid evolution equations of a closed vortex sheet in a plane, separating two piecewise constant density fluids, and their Hamiltonian form are investigated. The model has potential applications to problems involving the dynamics of interfaces of two immiscible fluids. A boundary Poisson bracket, which appears to be new and related to the KdV bracket, is obtained containing the curve-tangential derivative $\partial / \partial s$. Lagrangian invariants of the sheet motion by its self-induced velocity--the Cauchy principal value of the Biot-Savart integral--are also derived. |
| title | On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet |
| topic | Fluid Dynamics Other Condensed Matter Mathematical Physics Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2408.13462 |