Spatially growing waves, intermittency, and convective chaos in an open- flow system
type: Item
instance of: scholarly article
title: Spatially growing waves, intermittency, and convective chaos in an open- flow system
zbMATH Open document ID: 0611.76061
DOI: 10.1016/0167-2789(87)90103-5
author: Robert J. Deissler
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: We study a model open-flow system: the time-dependent generalized Ginzburg-Landau equation under conditions when it is convectively (i.e. spatially) unstable. In the presence of low-level external noise, this system exhibits a selective spatial amplification of noise resulting in spatially growing waves. Three distinct spatial regions are found: 1) A linear region in which spatially growing waves are formed; 2) a transition region characterized by the transition from the spatially growing wave frequencies of the linear region to the turbulent frequencies of the fully developed region; and 3) a fully developed region in which the nonlinear dynamics dominates. In the transition region, the microscopic noise plays an important role in the macroscopic dynamics of the system. In particular, the external noise initiates the transition to turbulence and is responsible for the intermittent turbulent behavior observed in the transition region. Power spectra and correlation functions are calculated and analytical expressions are derived for these quantities in the linear region. Similarities between this system and fluid systems are discussed. Also, a few analytical results for coupled-map lattices are derived.
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 76F99
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 35Q30
zbMATH DE Number: 3988956
zbMATH Keywords: fluid flow in a pipe
zbMATH Keywords: open-flow system
zbMATH Keywords: time-dependent generalized Ginzburg-Landau equation
zbMATH Keywords: low-level external noise
zbMATH Keywords: spatial amplification of noise
zbMATH Keywords: spatially growing waves
zbMATH Keywords: linear region
zbMATH Keywords: linear region to the turbulent frequencies
zbMATH Keywords: nonlinear dynamics
zbMATH Keywords: microscopic noise
zbMATH Keywords: macroscopic dynamics of the system
zbMATH Keywords: transition to turbulence
zbMATH Keywords: intermittent turbulent behavior
zbMATH Keywords: Power spectra
zbMATH Keywords: correlation functions
zbMATH Keywords: coupled-map lattices
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90103-5
OpenAlex ID: W2084577385
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description: scientific article; zbMATH DE number 3988956