Resonance and phase solitons in spatially-forced thermal convection
type: Item
instance of: scholarly article
title: Resonance and phase solitons in spatially-forced thermal convection
zbMATH Open document ID: 0621.76043
DOI: 10.1016/0167-2789(86)90107-7
author: P. Coullet
author: P. Huerre
published in: Physica D
publication date: 1986-01-01T00:00:00Z
review text: The competition between external and internal length scales is studied theoretically, on a two-dimensional amplitude evolution model of a fluid layer heated from below. A spatially-periodic excitation is applied to the stress-free, isothermal boundaries at a wavenumber close to the critical wavenumber for the onset of the instability. Near resonance, the large-scale phase dynamics give rise to stationary phase solitons at high Prandtl numbers and propagating sine-Gordon solitons at low Prandtl numbers. The propagating solitons are associated with the external breaking of the Galilean invariance of the problem.
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 76R05
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4007955
zbMATH Keywords: Overbeck-Boussinesq equation
zbMATH Keywords: two-dimensional amplitude evolution model
zbMATH Keywords: fluid layer
zbMATH Keywords: spatially-periodic excitation
zbMATH Keywords: stress-free, isothermal boundaries
zbMATH Keywords: onset of the instability
zbMATH Keywords: large-scale phase dynamics
zbMATH Keywords: stationary phase solitons
zbMATH Keywords: sine-Gordon solitons
zbMATH Keywords: Galilean invariance
MaRDI profile type: Publication
full work available at URL: 0167-2789(86)90107-7
OpenAlex ID: W2068954888
cites work: Hydrodynamic instabilities and the transition to turbulence
cites work: Q3744534
cites work: Thermal convection with spatially periodic boundary conditions: resonant wavelength excitation
cites work: Q3720105
cites work: Stability of finite-amplitude convection
cites work: Q4151274
cites work: Chemical oscillations, waves, and turbulence
cites work: Q3896709
cites work: Finite bandwidth, finite amplitude convection
cites work: Singular Perturbations of Bifurcations
cites work: Imperfect bifurcation in the presence of symmetry
cites work: Slowly Varying Waves and Shock Structures in Reaction-Diffusion Equations
cites work: Phase dynamics of weakly unstable periodic structures.
cites work: Convection patterns in large aspect ratio systems
cites work: The oscillatory instability of convection rolls in a low Prandtl number fluid
cites work: Transition to time-dependent convection
cites work: Viscoelastic behaviour of cellular solutions to the Kuramoto-Sivashinsky model
cites work: Q3889412
cites work: One-dimensional dislocations. I. Static theory
description: scientific article; zbMATH DE number 4007955