A Computational Study of the Dynamics of the Critical Points in a Simple Fluid Flow

TL;DR

This study uses computational methods to analyze how stagnation points in a simple fluid flow behave and transition at different Reynolds numbers, revealing two distinct stages of topological change.

Contribution

It provides a computational perspective on the topological transition of stagnation points in fluid flow, replicating experimental findings with detailed resolution.

Findings

Identification of two distinct stages of stagnation point annihilation.

Reynolds number range where annihilation rate increases sharply.

Validation of experimental phenomena through computational simulation.

Abstract

We carry out a computational experiment inspired by a physical experiment by Ouellette and Gollub (PRL 99, 194502 (2007)) where a topological transition of the velocity field in a fluid flow is generated by a grid of magnets. At a well-defined Reynolds number Re the motion of the stagnation points becomes so strong that they may merge and annihilate. Replacing the magnets by a grid of stirrers we obtain the same essential features of the transition, but the resolution allows us to identify two different stages of the process: A range of Re where the annihilation rate of the stagnation points is low but non-zero is followed by a narrow interval where the rate jumps to a high level.