A Seven Mode Truncation of the Kolmogorov Flow with Drag: Analysis and Control

The transition from laminar to chaotic motions in a viscous °uid °ow is in-vestigated by analyzing a seven dimensional dynamical system obtained by atruncation of the Fourier modes for the Kolmogorov °ow with drag friction. An-alytical expressions of the Hopf bifurcation curves are obtained and a sequenceof period doubling bifurcations are numerically observed as the Reynolds num-ber is increased for ¯xed values of the drag parameter. An adaptive stabilizationof the system trajectories to an equilibrium point or to a periodic orbit is ob-tained through a model reference approach which makes the control global.Finally, the e®ectiveness of this control strategy is numerically illustrated.