Structural Evolution of the Taylor Vortices

We classify in this article the structure and its transitions/evolution of the Taylor vortices with perturbations in one of the following categories: a) the Hamiltonian vector fields, b) the divergence-free vector fields, and c). the solutions of the Navier-Stokes equations on the two-dimensional torus. This is part of a project oriented toward to developing a geometric theory of incompressible fluid flows in the physical spaces