Lagrangian Description, Symplectic Structure, and Invariants of 3D Fluid Flow
solv-int
2009-10-30 v1 Exactly Solvable and Integrable Systems
Abstract
Three dimensional unsteady flow of fluids in the Lagrangian description is considered as an autonomous dynamical system in four dimensions. The condition for the existence of a symplectic structure on the extended space is the frozen field equations of the Eulerian description of motion. Integral invariants of symplectic flow are related to conservation laws of the dynamical equation. A scheme generating infinite families of symmetries and invariants is presented. For the Euler equations these invariants are shown to have a geometric origin in the description of flow as geodesic motion; they are also interpreted in connection with the particle relabelling symmetry.
Keywords
Cite
@article{arxiv.solv-int/9703012,
title = {Lagrangian Description, Symplectic Structure, and Invariants of 3D Fluid Flow},
author = {H. Gumral},
journal= {arXiv preprint arXiv:solv-int/9703012},
year = {2009}
}
Comments
Plain Latex, 15 pages