An investigation of chaotic Kolmogorov flows

A two-dimensional flow governed by the incompressible Navier–Stokes equations with a steady spatially periodic forcing (known as the Kolmogorov flow) is numerically simulated. The behavior of the flow and its transition states as the Reynolds number Re varies is investigated in detail, as well as a number of the flow features. A sequence of bifurcations is shown to take place in the flow as Re varied. Two main regimes of the flow have been observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of periodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with nonunique chaotic attractors. Spatially disordered, but temporally steady states have been discovered in the large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincaré sections and, where possible, Lyapunov exponents and Lyapunov dimension.