Non-equilibrium Pattern Modes Extracted from Experimental Data

Abstract

We describe a method to extract from experimental data the important dynamical modes in spatio-temporal patterns in a system driven out of thermodynamic equilibrium. Using a novel optical technique for controlling fluid flow, we create an experimental ensemble of Rayleigh-B\'{e}nard convection patterns with nearby initial conditions close to the onset of secondary instability. An analysis of the ensemble evolution reveals the spatial structure of the dominant modes of the system as well as the corresponding growth rates. The extracted modes are related to localized versions of instabilities found in the ideal unbounded system. The approach may prove useful in describing instability in experimental systems as a step toward prediction and control.