Convection in Binary Fluid Mixtures. II. Localized Traveling Waves. (Physical Review E, in press)

Abstract

Nonlinear, spatially localized structures of traveling convection rolls are investigated in quantitative detail as a function of Rayleigh number for two different Soret coupling strengths (separation ratios) with Lewis and Prandtl numbers characterizing ethanol-water mixtures. A finite-difference method was used to solve the full hydrodynamic field equations numerically. Structure and dynamics of these localized traveling waves (LTW) are dominated by the concentration field. Like in the spatially extended convective states ( cf. accompanying paper), the Soret-induced concentration variations strongly influence, via density changes, the buoyancy forces that drive convection. The spatio-temporal properties of this feed-back mechanism, involving boundary layers and concentration plumes, show that LTW's are strongly nonlinear states. Light intensity distributions are determined that can be observed in side-view shadowgraphs. Detailed analyses of all fields are made using colour-coded isoplots, among others. In the frame comoving with their drift velocity, LTW's display a nontrivial spatio-temporal symmetry consisting of time-translation by half an oscillation period combined with vertical reflection through the horizontal midplane of the layer. A time-averaged concentration current is driven by a phase difference between the waves of concentration and vertical velocity in the bulk of the LTW state. The associated large-scale concentration redistribution stabilizes the LTW and controls its drift velocity into the quiescent fluid by generating a buoyancy-reducing concentration "barrier" ahead of the leading LTW front. The selection of the width of the LTW's is investigated and comparisons with experiments are presented.