Instability and Turbulence of Wavefronts in Reaction-Diffusion Systems

Abstract

The theoretical possibility of a new kind of diffusion-induced chemical turbulence is discussed. Here the nearly planar wavefront of a pulse or phase-boundary propagating through a more than one-dimensional medium is of our concern. By means of an asymptotic method an equation describing the behavior of a curved wavefront is first derived assuming that its spatial variation is slow. The method employed and the resulting equation are completely analogous to those encountered in the theory of turbulent phase waves presented earlier, although the physical situations considered are different. It turns out that if a spontaneous deformation of a planar wavefront occurs, this is immediately accompanied by turbulence provided that the system is well extended. The condition for this kind of instability is shown analytically to be fulfilled by a simple activator-inhibitor model.