Statistical topology of the streamlines of a two-dimensional flow
Fluid Dynamics
2024-12-30 v2 Statistical Mechanics
Biological Physics
Abstract
Recent experiments on mucociliary clearance, an important defense against airborne pathogens, have raised questions about the topology of two-dimensional (2D) flows. 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.
Keywords
Cite
@article{arxiv.2110.10624,
title = {Statistical topology of the streamlines of a two-dimensional flow},
author = {M. Kamb and J. Byrum and G. Huber and G. Le Treut and S. Mehta and B. Veytsman and D. Yllanes},
journal= {arXiv preprint arXiv:2110.10624},
year = {2024}
}
Comments
7 pages, 3 figures