Symplectic Structures and Dynamics on Vortex Membranes
Symplectic Structures and Dynamics on Vortex Membranes
We present a Hamiltonian framework for higher-dimensional vortex filaments (or membranes) and vortex sheets as singular 2-forms with support of codimensions 2 and 1, respectively, i.e. singular elements of the dual to the Lie algebra of divergence-free vector fields.It turns out that the localized induction approximation (LIA) of the hydrodynamical …