Helicity current as a symplectic dilation

Details Helicity current as a symplectic dilation Helicity current as a symplectic dilation

1999-04-14

arxiv.org/abs/math-ph/9904012v1

Physics

Mathematical Physics

Latex, 9 page, submitted to Physics Letters A

Scientific paper

A formal symplectic structure on RxM is constructed for the unsteady flow of an incompressible viscous fluid on a three dimensional domain M. The evolution equation for the helicity density is expressed via the divergence of the Liouville vector field that generates symplectic dilation. For an inviscid fluid this equation reduces to a conservation law. As an application the symplectic dilation is used to generate Hamiltonian automorphisms of the symplectic structure which are then related to the symmetries of the velocity field.

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