An investigation of chaotic Kolmogorov flows
Abstract
A two dimensional flow governed by the incompressible NavierStokes 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 were observed: small and large scale structure regimes corresponding to different ranges of Re. Each of the regimes includes a number of quasiperiodic, chaotic, and relaminarization windows. In addition, each range contains a chaotic window with nonergodic chaotic attractors. Spatially disordered, but temporally steady states were discovered in large scale structure regime. Features of the diverse cases are displayed in terms of the temporal power spectrum, Poincare sections and, where possible, Lyapunov exponents and KaplanYorke dimension.
 Publication:

Final Report Institute for Computer Applications in Science and Engineering
 Pub Date:
 August 1990
 Bibcode:
 1990icas.reptR....P
 Keywords:

 Chaos;
 Incompressible Flow;
 NavierStokes Equation;
 Numerical Flow Visualization;
 Turbulence;
 Two Dimensional Flow;
 Mathematical Models;
 Reynolds Number;
 Steady State;
 Fluid Mechanics and Heat Transfer