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Prog. Theor. Phys. Vol. 106 No. 2 (2001) pp. 315-322

[ Full Text PDF : FREE ACCESS (133K) ]

Possibility of Soft-Mode Turbulence in Reaction-Diffusion Systems

Hirokazu Fujisaka1,* and Tomoji Yamada2,**

1Department of Applied Analysis and Complex Dynamical Systems
Graduate School of Informatics
Kyoto University, Kyoto 606-8501, Japan
2Division of Electronic Physics, Faculty of Engineering
Kyushu Institute of Technology, Kitakyushu 860-0862, Japan

(Received April 11, 2001)

Abstract:

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, \dot φ (r,t)=-∇2[ ε-(∇2+k02)2 ] φ+(∇φ)2. 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.


URL : http://ptp.ipap.jp/link?PTP/106/315/
DOI : 10.1143/PTP.106.315


*E-mail: fujisaka@i.kyoto-u.ac.jp
**E-mail: yamada@elcs.kyutech.ac.jp

[ Full Text PDF : FREE ACCESS (133K) ] Citation:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 75 (2006) 063801 (4 pages) :
    Control Parameter Dependence of Spatial Domain Structures in Soft-Mode Turbulence
    Koyo Tamura, Rinto Anugraha, Ryohei Matsuo, Yoshiki Hidaka and Shoichi Kai
  2. Journal of the Physical Society of Japan 79 (2010) 124004 (4 pages) :
    Modal and Total Power Spectra of Nikolaevskii Turbulence
    Dan Tanaka and Makoto Okamura
  3. Progress of Theoretical Physics Vol. 109 No. 6 (2003) pp. 911-918 :
    Amplitude Equation of Higher-Dimensional Nikolaevskii Turbulence
    Hirokazu Fujisaka, Tomoaki Honkawa and Tomoji Yamada
  4. Progress of Theoretical Physics Supplement No.161 (2006) pp. 1-11 :
    Soft-Mode Turbulence in Electroconvection of Nematics
    Yoshiki Hidaka, Koyo Tamura and Shoichi Kai
  5. Progress of Theoretical Physics Supplement No.161 (2006) pp. 119-126 :
    Turing Instability Leads Oscillatory Systems to Spatiotemporal Chaos
    Dan Tanaka

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