Diffusion-Induced Chemical Turbulence

Abstract

It is almost a common belief today that there exist such macroscopic phenomena that are certainly governed by deterministic chaos. Many of the chaotic phenomena appear as spatio-temporal chaos, and their adequate mathematical modeling often calls for a set of partial differential equations. In the past, the studies of spatio-temporal chaos have largely been concerned with a variety of turbulent phenomena in fluid systems [1,2] obeying the Navier-Stokes equation. Recent studies made it clear that a much simpler class of partial differential equations called reaction-diffusion equations is also capable of showing complicated space-time behavior. This was demonstrated for the Brussels model [3–5], the Rashevsky-Turing model [6], and also for a still wider class of systems consisting of diffusion-coupled oscillators [3–10]. In view of the surprising richness of patterns which reaction-diffusion equations can exhibit, it is quite natural to expect that chemical turbulence of diffusion-induced type could hardly be confined to the kinds discovered so far. The purpose of the present paper is to explore the possibility of a novel class of chemical turbulence, in particular, the one associated with the wavefront behavior of some chemical waves in media with the spatial dimension two.