Experimental studies of binary fluid convection patterns in one and two dimensions.

摘要

Convection in binary fluid mixtures provides a model system in which to study patterns of traveling waves. We study patterns near the onset of convection, where the convection takes the form of locally parallel "rolls" of alternating upflowing and downflowing regions. This roll pattern constrains the flow patterns in the vertical direction, with the flow pattern at the vertical midplane determining the entire flow. Thus, the vertical extent of the system is not needed to describe the pattern dynamics and we can describe the system by a reduced two-dimensional system. By further restricting the geometry to suppress transverse modulations along the roll axes, an effectively one-dimensional system results. Several experiments in one-dimensional and two-dimensional geometries are presented. A study of the concentration field in binary fluid convection in a one-dimensional cell confirmed the existence of a concentration modulation between adjacent rolls which is responsible for the traveling-wave motion of the pattern. Comparison with numerical simulations verified several properties of the concentration field. As the Rayleigh number increases, the concentration modulation between rolls decreases in magnitude and goes to zero at the traveling-wave to stationary overturning convection transition. Another study focused on the Eckhaus instability for traveling waves in an annular geometry. It was found that propagating wave number modulations mediate the transition between states of different average wave number. The propagation characteristics of the modulations are consistent with the measured dispersion relation and dominate the manner in which the instability evolves in space and time. The design, construction, and testing of an apparatus to study traveling-wave convection in a large-aspect-ratio two-dimensional geometry is described. An experimental survey of the system has revealed a novel, two-dimensional globally rotating state which consists of multiple domains of traveling waves. A study of the traveling wave frequency versus Rayleigh number is in qualitative agreement with theoretical predictions. Finally, a new transition is described which occurs at high Rayleigh number when the pattern is stationary. In this transition, the curved roll patterns change to a rectilinear pattern consisting of disclinations and arches connected by straight rolls.