Spiral instabilities in periodically forced and chaotic media
by
Markus Baer
Max-Planck-Institute for the Physics of Complex Systems

Spiral instabilities in periodically forced and chaotic media

We report three novel spiral instabilities that go beyond the well-known cases of far-field and core breakup of simple rotating spirals. In all cases, we compare the phenomenology found in numerical simulations with results from numerical stability analysis. For periodic forcing of a spiral in the complex Ginzburg-Landau equation CGLE by external variations or core instabilities like meandering, we observe superspirals of amplitude modulations that decay, grow or increase with the distance from the spiral core. A numerical bifurcation analysis relates the scenarios to the existence of modulated amplitude waves. We conjecture a saddle-node bifurcation of superspirals from the bifurcation diagram of the modulated amplitude waves (joint work with Lutz Brusch and Alessandro Torcini). For a resonantly forced CGLE, we show that spirals are destabilized in the 1:2 case upon increasing the forcing beyond a critical threshold. A numerical stability analysis reveals that the forcing destabilizes wave trains due to attraction of subsequent fronts and merging. The role of convective and absolute instabilities is considered (joint work with Hwa-Kyun Park). In chaotic media, spirals may become unstable against the formation of a defect line. This instability is related to a periodic doubling instability of wavetrains which is discussed in some detail (joint work with Joern Davidsen and Ray Kapral).

Date received: May 28, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calo-18.