6533b852fe1ef96bd12aad8d
RESEARCH PRODUCT
A Seven Mode Truncation of the Kolmogorov Flow with Drag: Analysis and Control
Marco SammartinoMaria Carmela LombardoGaetana Gambinosubject
Period-doubling bifurcationEquilibrium pointHopf bifurcationTruncationMathematical analysisReynolds numberLaminar flowDynamical systemPhysics::Fluid Dynamicssymbols.namesakeClassical mechanicsDragsymbolsKolmogorov flow finite dimensional approximation adaptive controlMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-05-01 |