Statistical topology of the streamlines of a two-dimensional flow

Abstract Recent experiments on mucociliary clearance, an important defense against airborne pathogens, have raised questions about the topology of two-dimensional (2D) flows, such as proportion topologically closed and open streamlines. We introduce a framework for studying ensembles 2D time-invariant flow fields estimating probability particle to leave finite area (to clear out). establish two upper bounds this by leveraging different insights distribution velocities also deduce exact power-series expression trapped based asymptotic dynamics flow-field trajectories complement our analytical results with numerical simulations.