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 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.