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Helicity invariants in 3D : kinematical aspects | | Hasan Gümral
; | | Date: |
11 Dec 1998 | | Subject: | Mathematical Physics | math-ph math.MP | | Affiliation: | Feza Gürsey Institute, Istanbul | | Abstract: | Exact, degenerate two-forms on time-extended space R X M which are invariant under the unsteady, incompressible fluid motion on 3D region M are introduced. The equivalence class up to exact one-forms of each potential one-form is splitted by the velocity field. The components of this splitting corresponds to Lagrangian and Eulerian conservation laws for helicity densities. These are expressed as the closure of three-forms which depend on two discrete and a continuous parameter. Each two-form is extended to a symplectic form on R X M. The subclasses of potential one-forms giving rise to Eulerian helicity conservations is shown to result in conformally symplectic structures on R X M. The connection between Lagrangian and Eulerian conservation laws for helicity is shown to be the same as the conformal equivalence of a Poisson bracket algebra to infinitely many local Lie algebra of functions on R X M. | | Source: | arXiv, math-ph/9812007 | | Services: | Forum | Review | PDF | Favorites | |
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