Fully developed traveling-wave convection in binary fluid mixtures

Abstract

Structural and dynamical properties of nonlinear traveling-wave states in binary fluid layers heated from below are determined by numerical integration of the proper hydrodynamic field equations with experimental horizontal boundary conditions. The fluid separates into traveling rolls of alternating high and low concentration. Phase differences drive lateral currents and Reynolds stresses lateral mean flow.

Confined states in large-aspect-ratio thermosolutal convection

“…Although of modest amplitude these solutions reveal that both O and £ have a trapezoidal, highly nonharmonic shape that cannot be described quantitatively by a weakly nonlinear expansion near onset [15,16]. In these states all the fields have the "mirror-…”

“…which is a combination of a translation by half a wavelength in the x direction with a mirror reflection through the z = ½ plane [2,[14][15][16]. This symmetry persists even at large Rayleigh numbers as long as the number of roll pairs is conserved during their time evolution.…”

“…indicating the fact that the absolute value of the phase is arbitrary, and the discrete "mirror-glide" symmetry [2,[14][15][16]. If the wave train has period 27r/k this symmetry acts by…”

“…The propagation speeds of the rolls inside and outside the pulses were computed by tracking zeros of the stream function • at midlayer. The presence of a "mirror-glide" symmetry [2,[14][15][16] makes the midline the natural place for these measurements. Finally, moving averages of several of the fields have been obtained.…”

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

“…The phase shift between the concentration and velocity waves in the TW-like bulk of the front states sustains as in extended TW states a mean lateral concentration current [24,25,68,69]:…”