Describing Chaotic Dynamics in Experimental Rayleigh-B\'enard Convection Using Persistent Homology Theory*

We employ a new technique for describing the dynamics of spatiotemporal chaos in Rayleigh-B\'enard convection. We collect shadowgraph images of multiple time series of weakly chaotic flows, each starting from similar initial conditions which we impose using a laser. We then encode the topological characteristics of each frame into a so-called persistence diagram, measure the distance across all diagrams, and study the dynamical behavior. Results are compared to similar analyses of simulation data. This new methodology provides unique insight into the time evolution of this dynamical system and the chaotic evolution across separate runs, in both experiment and simulation.