Benjamin-Feir turbulence in convective binary fluid mixtures
type: Item
instance of: scholarly article
title: Benjamin-Feir turbulence in convective binary fluid mixtures
zbMATH Open document ID: 0621.76057
DOI: 10.1016/0167-2789(86)90140-5
author: Helmut R. Brand
author: Alan C. Newell
author: Peter S. Lomdahl
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: Binary mixtures of water and alcohol provide an excellent vehicle for studying the onset of a rich variety of dynamical behavior. For different values of the separation ratio, these systems exhibit both steady and oscillatory convection, competition between the two, and in another parameter range, a weakly turbulent state. We develop a general theory which is valid near onset and which can account for each of these features. A universal equation of Ginzburg-Landau type with complex coefficients obtains and is investigated numerically and analytically in one and two spatial dimensions. The most novel prediction is that some of the a periodic behavior seen in experiment is due to the universal Benjamin-Feir instability and we call this phenomenon Benjamin-Feir turbulence [\textit{T. B. Benjamin} and \textit{J. E. Feir}, J. Fluid Mech. 27, 417-430 (1967; Zbl 0144.471)]. Although the possibility of this effect has been discussed theoretically in the literature for over ten years, binary mixture convection provides the first vehicle in which the prediction can be quantitatively tested. We also discuss mean drift effects and the consequences of fixed lateral boundaries.
Mathematics Subject Classification ID: 76E30
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 76T99
Mathematics Subject Classification ID: 76F99
zbMATH DE Number: 4007969
zbMATH Keywords: Hopf bifurcation
zbMATH Keywords: oscillatory convection
zbMATH Keywords: weakly turbulent state
zbMATH Keywords: equation of Ginzburg-Landau type
zbMATH Keywords: universal Benjamin-Feir instability
zbMATH Keywords: Benjamin-Feir turbulence
zbMATH Keywords: binary mixture convection
zbMATH Keywords: mean drift effects
zbMATH Keywords: fixed lateral boundaries
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90140-5
OpenAlex ID: W2087030126
cites work: Q4199144
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description: scientific article; zbMATH DE number 4007969