On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet

Banavara N. Shashikanth

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arXiv · 2408.13462

On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet

Banavara N. Shashikanth

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Abstract

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.

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Banavara N. Shashikanth. 2024-08-24. On the Hamiltonian structure of the intrinsic evolution of a closed vortex sheet. https://arxiv.org/abs/2408.13462

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