Examining departures from the Boussinesq approximation in chaotic Rayleigh-Benard convection using persistent homology

Persistent homology is a data analysis technique that can be used to quantify the topological information of image data. In the spatio-temporally chaotic flow known as spiral defect chaos in Rayleigh-Benard convection, we explore the connection between convective plumes detected by persistent homology and the extent that the flow deviates from the Boussinesq approximation, a common simplification used to study convective flows. Simulations of the Boussinesq approximation predict that hot and cold plumes occur at roughly equal rates over time scales comparable to the horizontal diffusion time. However, using the same mean values of physical parameters, we demonstrate that rates of hot and cold plume formation differ in simulations and experiments that deviate from the Boussinesq approximation.