Vorticity generation by the instantaneous release of energy near a reflective boundary.

The instantaneous release of energy in a localized area of a gas results in the formation of a low-density region and a series of shock and expansion waves. If this process occurs near a boundary, the shock reflections can interact with the density inhomogeneity, leading to the baroclinic generation of vorticity and the subsequent organization of the flow into several structures, including a vortex ring. By means of numerical simulations we illustrate the qualitative changes that occur in the pressure wave patterns and vorticity distribution as the distance from the area of energy release to the boundary is varied. Those changes are shown to be related to the combined effect of the shock waves that, respectively, initially move away and towards the center of the low-density region. In particular, we describe how for small enough offset distances the shocks internal to the inhomogeneity can make a substantial contribution to the vorticity field, influencing the circulation and characteristics of the resulting flow structures.

Route to hyperchaos in a system of coupled oscillators with multistability.

This work presents the results of a detailed experimental study into the transition between synchronized, low-dimensional, and unsynchronized, high-dimensional dynamics using a system of coupled electronic chaotic oscillators. Novel data analysis techniques have been employed to reveal that a hyperchaotic attractor can arise from the amalgamation of two nonattracting sets. These originate from initially multistable low-dimensional attractors which experience a smooth transition from low- to high-dimensional chaotic behavior, losing stability through a bubbling bifurcation. Numerical techniques were also employed to verify and expand on the experimental results, giving evidence on the locally unstable invariant sets contained within the globally stable hyperchaotic attractor. This particular route to hyperchaos also results in the possibility of phenomena (such as unstable dimension variability) that can be a major obstruction to shadowing and predictability in chaotic systems.

Method for measuring unstable dimension variability from time series.

Many of the results in the theory of dynamical systems rely on the assumption of hyperbolicity. One of the possible violations of this condition is the presence of unstable dimension variability (UDV), i.e., the existence in a chaotic attractor of sets of unstable periodic orbits, each with a different number of expanding directions. It has been shown that the presence of UDV poses severe limitations to the length of time for which a numerically generated orbit can be assumed to lie close to a true trajectory of such systems (the shadowing time). In this work we propose a method to detect the presence of UDV in real systems from time series measurements. Variations in the number of expanding directions are detected by determining the local topological dimension of the unstable space for points along a trajectory on the attractor. We show for a physical system of coupled electronic oscillators that with this method it is possible to decompose attractors into subsets with different unstable dimension and from this gain insight into the times a typical trajectory spends in each region.