Phase-space analysis of bursting behavior in Kolmogorov flow

PDE simulations for the Kolmogorov flow are analyzed in terms of phase-space concepts. The tool used is the proper orthogonal decomposition method which extracts coherent structures and prominent features of a random or turbulent dataset. We analyze a quasiperiodic regime and an intermittent regime. We derive two eigenfunctions that determine the dynamics and structure of the quasiperiodic case and find a third one associated with the unstable manifold of the bursts of the intermittent regime. Calculations are performed for streamfunction data and vorticity data which show substantial differences. It is argued that the streamfunction data demonstrate the low dimensional phase-space dynamics of the large scales whereas the vorticity data show an enstrophy cascade.