Using topology to identify large Lyapunov vector magnitude in Rayleigh-Bénard 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-Bénard convection, we investigate how pattern features detected in laboratory experiments can be related to leading-order Lyapunov vectors computed from convection simulations. In particular, we demonstrate that convective plumes, detected using persistent homology, are strongly correlated to spatially-localized regions of high magnitude of leading-order Lyapunov vectors in simulations. Additionally, we show that plume statistics are similar for both patterns in experiments and in simulations at the same parameter values. These results suggest that plumes detected by persistent homology reliably indicate spatial locations in convection experiments that are sensitive to small disturbances.