Quasiperiodic routes to chaos in confined two-dimensional differential convection.

The complete cascade of bifurcations from steady to chaotic convection, as the Rayleigh number is varied, is considered numerically inside an air-filled differentially heated cavity. The system is assumed to be two-dimensional and is invariant under a generalized reflection about the center of the cavity. In the neighborhood of several codimension-two points, two main routes emerge, characterized by different symmetries of the first oscillatory eigenstate. Along these two competing routes, different sequences of bifurcations and symmetry breakings lead from the steady base flow to the hyperchaotic regime. Several families of two- and three-frequency tori have been identified via the computation of the leading Lyapunov exponents. Modal structures extracted from time series reveal the occurrence of slow internal oscillations in the center of the cavity and faster wall modes confined to vertical boundary layers. Further quasiperiodicity windows have been detected on each route. The different regimes eventually disappear in a boundary crisis in favor of a single, globally symmetric, hyperchaotic regime.

Imperfect supercritical bifurcation in a three-dimensional turbulent wake.

The turbulent wake of a square-back body exhibits a strong bimodal behavior. The wake randomly undergoes symmetry-breaking reversals between two mirror asymmetric steady modes [reflectional symmetry-breaking (RSB) modes]. The characteristic time for reversals is about 2 or 3 orders of magnitude larger than the natural time for vortex shedding. Studying the effects of the proximity of a ground wall together with the Reynolds number, it is shown that the bimodal behavior is the result of an imperfect pitchfork bifurcation. The RSB modes correspond to the two stable bifurcated branches resulting from an instability of the stable symmetric wake. An attempt to stabilize the unstable symmetric wake is investigated using a passive control technique. Although the controlled wake still exhibits strong fluctuations, the bimodal behavior is suppressed and the drag reduced. This promising experiment indicates the possible existence of an unstable solution branch corresponding to a reflectional symmetry preserved (RSP) mode. This work is encouraging to develop a control strategy based on a stabilization of this RSP mode to reduce mean drag and lateral force fluctuations.

Defects in spatiotemporal diagrams and their relations to phase coherence and lack of observability.

Spatiotemporal systems are commonly investigated in terms of spatiotemporal diagrams and, most often, the analysis is limited to the first instabilities. Due to the lack of a Takens-like theorem for spatiotemporal systems, the resulting dynamics is almost never interpreted using phase portraits reconstructed from one variable locally recorded. This work is an attempt to make an explicit link between reconstructed phase portraits and spatiotemporal diagrams. Defects distributions are interpreted in terms of a lack of phase coherence. The lack of a simple structure--as a torus characterized by a closed curve for Poincaré section when a quasiperiodic regime is identified--is tentatively interpreted in terms of observability. A first link is thus made between the defects distribution and the nature of the underlying dynamics.

Sources and holes in a one-dimensional traveling-wave convection experiment.

We study dynamical behavior of local structures, such as sources and holes, in traveling-wave patterns in a very long (2 m) heated wire convection experiment. The sources undergo a transition from stable coherent behavior to erratic behavior when the driving parameter epsilon is decreased. This transition, as well as the scaling of the average source width in the erratic regime are both qualitatively and quantitatively in accord with earlier theoretical predictions. We also present results for the holes sent out by the erratic sources.