Longwave convection in a layer of binary mixture with modulated heat flux: weakly nonlinear analysis

We consider dynamics of a binary mixture layer subject to a modulated heat flux at the bottom. Nonlinear evolution for longwave synchronous mode is shown to be governed by a set of nonlocal amplitude equations, solvability conditions of a certain linear nonhomogeneous problem. For the superlattice c...

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Published inFluid dynamics research Vol. 46; no. 4; pp. 41411 - 20
Main Authors Fayzrakhmanova, Irina S, Shklyaev, Sergey, Nepomnyashchy, Alexander A
Format Journal Article
LanguageEnglish
Published IOP Publishing 01.08.2014
Subjects
Binary mixtures
Heat flux
Heat transfer
Hexagonal lattice
Mathematical analysis
Nonlinear dynamics
Nonlinearity
Superlattices
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Summary:We consider dynamics of a binary mixture layer subject to a modulated heat flux at the bottom. Nonlinear evolution for longwave synchronous mode is shown to be governed by a set of nonlocal amplitude equations, solvability conditions of a certain linear nonhomogeneous problem. For the superlattice combining two hexagonal lattices, the set of nonlocal equations can be reduced to the set of Landau equations with cubic and quadratic nonlinear terms. Although this set is conventional for a small-amplitude analysis, in the present work it is valid even for finite-amplitude regimes; the perturbations of both temperature and solute concentration are of order unity, only their gradients are small. Nontrivial matching with known limiting cases is found.
Bibliography:The Japan Society of Fluid Mechanics
ObjectType-Article-1
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ISSN:0169-5983
1873-7005
DOI:10.1088/0169-5983/46/4/041411