Dynamics and Routes to Chaos from Quasiperiodicity,
ADVISORY GROUP FOR AEROSPACE RESEARCH AND DEVELOPMENT NEUILLY-SUR-SEINE (FRAN CE)
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One of the routes leading to deterministic chaos is the route through quasiperiodicity the simplest one involves the presence of two oscillators, whose dynamics may become chaotic by the increase of the amount of the non-linearities between them. Though this dynamics is generally related to non-linear dynamical systems, it may be found in hydrodynamical flows, as soon as the increase of a control parameter Reynolds number, Rayleigh number, etc... initiates the appearance of periodic behaviors. In this report, the physical examples are taken from Rayleigh-Benard experiments, which provide good illustrations of quasiperiodic behaviors in dissipative systems. Topics include Quasiperiodicity in Rayleigh-Benard convection Quasiperiodic models Dynamical properties near the critical line -- Phase intermittencies, Direct route from quasiperiodicity to chaos, and Two oscillators evolution in a free Rayleigh-Benard experiment and Dynamics inside the phase locked tongues.
- Fluid Mechanics