Spatial-Feedback Control of Dispersive Chaos in Binary-Fluid Convection

Dispersive chaos is an erratic state of traveling-wave (TW) convection that is observed in a long, quasi-one-dimensional cell containing a binary fluid with small, negative separation ratio which is heated from below. This state consists of the repeated, irregular growth and abrupt decay of spatially-localized bursts of TW and is observed over a narrow range of Rayleigh numbers just above the onset of convection. We describe experiments in which this erratic behavior is suppressed by applying as feedback a spatially-varying Rayleigh-number profile computed from the measured convection pattern. With the appropriate feedback algorithm, an initial state consisting of unidirectional TW of spatially-uniform amplitude and wave number can be maintained in a steady state over a large fraction of the unstable branch of the subcritical bifurcation to convection. This allows us to measure the nonlinear coefficients of the corresponding quintic complex Ginzburg-Landau equation.