Using Persistent Homology to Compare Chaotic Dynamics Between Experiments on and Simulations of Rayleigh-B\'enard Convection

Persistent homology is a tool from algebraic topology that can be used to efficiently detect pattern features in image data. In the spatio-temporally chaotic flow known as spiral defect chaos in Rayleigh-B\'enard convection, we explore the use of pattern features detected by persistent homology as a proxy for fundamental dynamical quantities that are not observable in experimental data but can be calculated from simulations, such as leading-order Lyapunov vectors. In simulations, we have identified that convective plumes are highly correlated with the leading-order Lyapunov vectors; however, we find that plumes appear in experiments at distinctly different rates than for Boussinesq simulations at the same parameter values. We describe work to resolve this discrepancy by accounting for non-Boussinesq effects in both experiments and simulations.