Journal of Statistical Physics

, Volume 40, Issue 3, pp 371–395

Noise-sustained structure, intermittency, and the Ginzburg-Landau equation

  • Robert J. Deissler

DOI: 10.1007/BF01017180

Cite this article as:
Deissler, R.J. J Stat Phys (1985) 40: 371. doi:10.1007/BF01017180


The time-dependent generalized Ginzburg-Landau equation is an equation that is related to many physical systems. Solutions of this equation in the presence of low-level external noise are studied. Numerical solutions of this equation in thestationary frame of reference and with anonzero group velocity that is greater than a critical velocity exhibit a selective spatial amplification of noise resulting in spatially growing waves. These waves in turn result in the formation of a dynamic structure. It is found that themicroscopic noise plays an important role in themacroscopic dynamics of the system. For certain parameter values the system exhibits intermittent turbulent behavior in which the random nature of the external noise plays a crucial role. A mechanism which may be responsible for the intermittent turbulence occurring in some fluid systems is suggested.

Key words

Dynamical systems nonlinear dynamics chaos turbulence intermittent turbulence intermittency noise external noise fluctuations external fluctuations Ginzburg-Landau equation amplitude equation spatially growing waves convective instability spatial instability secondary instability noise-sustained structure noise amplification spatial noise amplification pattern formation 

Copyright information

© Plenum Publishing Corporation 1985

Authors and Affiliations

  • Robert J. Deissler
    • 1
  1. 1.Los Alamos National LaboratoryCenter for Nonlinear Studies, MS B258Los Alamos
  2. 2.Physics DepartmentUniversity of California at Santa CruzSanta Cruz

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