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-Siv...

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Bibliographic Details
Published in:Progress of theoretical and experimental physics 2001-08, Vol.106 (2), p.315-322
Main Authors: Fujisaka, Hirokazu, Yamada, Tomoji
Format: Article
Language:English
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Summary: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 k 0 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.
ISSN:0033-068X
2050-3911
1347-4081
DOI:10.1143/PTP.106.315