Year: 1999
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Gumral, Hasan
Institution: Feza Gürsey Institute
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1799801613