Convection in binary fluid mixtures: Traveling waves and lateral currents

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Abstract
We investigate currents of heat, concentration, and mass in binary fluid layers heated from below. In particular, we investigate traveling waves (TW’s) of laterally propagating convective roll patterns. We present nonlinear analytical TW solutions of a simple Galerkin model for impermeable horizontal boundary conditions. Bifurcation properties, stability, existence range, and the spatial field profiles of TW’s are determined for negative and positive separation ratios. The temperature wave lags behind and the concentration wave runs ahead of the wave in the vertical velocity. These phase differences imply time-independent global currents: in the upper half of the layer there is a lateral heat flow opposite to the TW and concentration flows parallel to it and vice versa in the lower half of the layer. Depending on where passive marked particles are injected they move together with a TW, or slower, or even backwards without there being a finite net mass transport. Finally we investigate whether the Reynolds stresses of a TW induce a mean lateral fluid flow.