Huseyin Kurtuldu

Homology and symmetry breaking in Rayleigh-Bénard convection: Experiments and simulations

Algebraic topology (homology) is used to analyze the state of spiral defect chaos in both laboratory experiments and numerical simulations of Rayleigh-Benard convection. The analysis reveals topological asymmetries that arise when non-Boussinesq effects are present. The asymmetries are found in different flow fields in the simulations and are robust to substantial alterations to flow visualization conditions in the experiment. However, the asymmetries are not observable using conventional statistical measures. These results suggest homology may provide a new and general approach for connecting spatiotemporal observations of chaotic or turbulent patterns to theoretical models.

State and parameter estimation of spatiotemporally chaotic systems illustrated by an application to Rayleigh–Bénard convection

Data assimilation refers to the process of estimating a systems state from a time series of measurements (which may be noisy or incomplete) in conjunction with a model for the systems time evolution. Here we demonstrate the applicability of a recently developed data assimilation method, the local ensemble transform Kalman filter, to nonlinear, high-dimensional, spatiotemporally chaotic flows in Rayleigh-Bénard convection experiments. Using this technique we are able to extract the full temperature and velocity fields from a time series of shadowgraph measurements. In addition, we describe extensions of the algorithm for estimating model parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of experimental situations exhibiting spatiotemporal chaos.