Possibility of Soft-Mode Turbulence in Reaction-Diffusion Systems

We propose the possibility of the observation of soft-mode turbulence in reaction-diffusion systems. Assuming that spatially uniform temporal oscillation becomes unstable with respect to short wavelength modes, we derive the reduced equation for phase dynamics, . In contrast to that the Kuramoto-Sivashinsky equation, which has unstable modes in the region of long wavelength fluctuations, the present phase equation has unstable modes in a short wavelength region near a finite wavenumber k0 for ϵ>0. In a one-dimensional system, the above is known as an equation exhibiting turbulent behavior (soft-mode turbulence). The new equation generalizes such turbulence to higher dimensions.