Symmetries and dynamics for 2-D Navier-Stokes flow

Simulations of forced 2-D Navier-Stokes equations are analyzed. The forcing is spatially periodic and temporally steady. A Karhunen-Loève analysis is used to identify the structures in phase space that generate the PDE behavior. Their relationship to the invariant subspaces generated by the symmetry group is discussed. It is shown that certain modes that are in the stable eigenspace of the Kolmogorov flow solution play an essential role for the dynamics of the attractor for the 2-D Navier-Stokes equations below a Reynolds number of about 30. In this regime all stable solutions are identified and their relation to the symmetry structure is elucidated. A new type of gluing bifurcation generated by the symmetry is found and analyzed. A mechanism for the generation of bursting behavior is suggested.