Three-dimensional twisted vortices in an excitable chemical medium

Abstract

SEVERAL different types of three-dimensional nonlinear wave structure are expected to occur in chemically excitable media1. In general these are vortex-like structures (Fig. 1, for example) in which the waves adopt complex spatial configurations (curved, knotted, twisted or closed into rings). But until recently only simple vortices and vortex rings have been observed experimentally, for example in the Belousov–Zhabotinsky (B–Z) reaction2–4 and in cardiac tissue5. Here we report a new type of structure, twisted vortices, observed in a B–Z reaction immobilized in agarose gel (Fig. 2). In cross-section, a twisted vortex resembles a rotating spiral with a phase of rotation that changes along the filament. The filament extends through the entire medium, terminating at its free surfaces. The wavelength of a twisted vortex is shorter than that of a simple one and decreases with increasing twist, in accord with theory6,7. The period shows little dependence on twist, contrary to the results of computer experiments6. Twisted vortices decay into simple ones; their twist decays exponentially with a time constant that increases with filament length. These dynamics are consistent with the theory of diffusional untwisting8,9 rather than that of shock waves10.