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MARIA CARMELA LOMBARDO

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

  • Autori: GAMBINO, G; LOMBARDO, MC; SAMMARTINO, MML
  • Anno di pubblicazione: 2009
  • Tipologia: eedings
  • Parole Chiave: Kolmogorov flow, finite dimensional approximation, adaptive control
  • OA Link: http://hdl.handle.net/10447/39994

Abstract

The transition from laminar to chaotic motions in a viscous °uid °ow is in- vestigated by analyzing a seven dimensional dynamical system obtained by a truncation of the Fourier modes for the Kolmogorov °ow with drag friction. An- alytical expressions of the Hopf bifurcation curves are obtained and a sequence of period doubling bifurcations are numerically observed as the Reynolds num- ber is increased for ¯xed values of the drag parameter. An adaptive stabilization of 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.