Mathematical tools based on algebraic topology (homology) provide new ways to
describe complex patterns of fluid flow observed in laboratory experiments.
First, we will discuss how homology can be used to quantify
non-Oberbeck-Boussinesq (NOB) effects in weakly turbulent Rayleigh-Benard convection patterns.
We then will describe homology-based methods to measure dynamical
finite-size effects in spatiotemporally-chaotic convective flows. Finally, we will