Statistical topology of the streamlines of a two-dimensional flow. (16th December 2022)

• Record Type: Journal Article
• Authors: Kamb, Mason; Byrum, Janie; Huber, Greg; Le Treut, Guillaume; Mehta, Shalin; Veytsman, Boris; Yllanes, David
• Is Part Of: Journal of physics. Volume 55:Number 50(2022)
• Publication Date: 2022-12-16
• Subjects: biological fluid dynamics -- statistical mechanics -- critical phenomena -- statistical hydrodynamics; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aca940
• Languages: English
• ISSNs: 1751-8113

Abstract

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 the proportion of topologically closed and open streamlines. We introduce a framework for studying ensembles of 2D time-invariant flow fields and estimating the probability for a particle to leave a finite area (to clear out). We establish two upper bounds on this probability by leveraging different insights about the distribution of flow velocities on the closed and open streamlines. We also deduce an exact power-series expression for the trapped area based on the asymptotic dynamics of flow-field trajectories and complement our analytical results with numerical simulations.