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Research

My research as a graduate student and all my research since then has involved table top, conceptually simple experiments. In this style of research a graduate student can design and build the experiment and collect and interpret the data. The results can be compared with predictions of exisiting theory, or the student can develop a mathematical model to gain insight into the laboratory observations.

The problems that my students and I have studied since I came to the University of Texas in 1978 have concerned instabilities, chaos, pattern formation, and turbulence in systems driven away from equilibrium by the imposition of gradients in temperature, velocity, concentration, etc. We search for an understanding of dynamical behavior that is similar in diverse systems. Problems examined in the past two decades include chaos and pattern formation in flow between concentric rotating cylinders (the “Couette-Taylor” system); chaos and strange attractors in oscillating chemical reactions; a laboratory model of Jupiter’s Great Red Spot; a laboratory model of the atmospheric “blocking” phenomenon; turbulence in buoyancy driven convection; pattern formation in surface-tension-driven (“Marangoni”) convection; growth of metallic fractal clusters in electrodeposition; chemical patterns of the type predicted by Alan Turing in his 1952 paper “The Chemical Basis for Morphogenesis”; other patterns in chemical reaction-diffusion systems, including reactions that are periodically forced in time, where “Arnold tongue” type phase diagrams have been found; vertically oscillated containers of grains (sand, metallic particles, etc.), which exhibit square, stripe, hexagon, spiral, and oscillon (localized) patterns.

Our current research examines shock waves in supersonic sand; the determination of statistical properties of rapid granular flows, where the observations are compared to the predictions of kinetic theory and continuum theory; instabilities in fluidized beds, where a fluid flows upward through a granular bed, such as in a gasoline refinery catalytic cracker; formation of “viscous finger” patterns at the interface between immiscible fluids; buckling of thin sheets (plastic, leaves of plants); and scaling and transport in rapidly rotating turbulent flows, such as those in oceans and atmospheres.