Abstract
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.
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Deissler, R.J. Noise-sustained structure, intermittency, and the Ginzburg-Landau equation. J Stat Phys 40, 371–395 (1985). https://doi.org/10.1007/BF01017180
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DOI: https://doi.org/10.1007/BF01017180
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