Hamiltonian formulation of adiabatic free boundary Euler flows

Authors

Arthur Mazer, Tudor Ratiu

Abstract

A Hamiltonian formulation of adiabatic free boundary inviscid fluid flow using only physical variables is presented in both the material and spatial formulation. Using the symmetry of particle relabeling, we derive the noncanonical Poisson bracket in Eulerian representation as a reduction from the canonical bracket in Lagrangian representation. When the free boundary of the fluid is given as the zero set of a function dragged along by the fluid flow, there is another bracket due to Abarbanel et al. [Physics of Fluids, (vol. 31), (2802), (1988)]. It is shown that this formulation «coverså the present one by proving that the natural restriction map is Poisson. It is also shown that the potential vortycity and the conserved quantities found by Abarbanel and Holm [Physics of Fluids (vol. 30), (3369), (1987)] are also conserved in the free boundary case.

Keywords

Hamiltonian formulation; Euler flows

Citation

• Journal: Journal of Geometry and Physics
• Year: 1989
• Volume: 6
• Issue: 2
• Pages: 271–291
• Publisher: Elsevier BV
• DOI: 10.1016/0393-0440(89)90017-x

BibTeX

@article{Mazer_1989,
  title={{Hamiltonian formulation of adiabatic free boundary Euler flows}},
  volume={6},
  ISSN={0393-0440},
  DOI={10.1016/0393-0440(89)90017-x},
  number={2},
  journal={Journal of Geometry and Physics},
  publisher={Elsevier BV},
  author={Mazer, Arthur and Ratiu, Tudor},
  year={1989},
  pages={271--291}
}

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