Related Experiment Video
Updated: Jul 2, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Onset of chaotic advection in open flows
J J Benjamin Biemond1, Alessandro P S de Moura, György Károlyi
1Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands.
Abstract:
In this paper we investigate the transition to chaos in the motion of particles advected by open flows with obstacles. By means of a topological argument, we show that the separation points on the surface of the obstacle imply the existence of a saddle point downstream from the obstacle, with an associated heteroclinic orbit. We argue that as soon as the flow becomes time periodic, these orbits give rise to heteroclinic tangles, causing passively advected particles to experience transient chaos. The transition to chaos thus coincides with the onset of time dependence in open flows with stagnant points, in contrast with flows with no stagnant points. We also show that the nonhyperbolic nature of the dynamics near the walls causes anomalous scalings in the vicinity of the transition. These results are confirmed by numerical simulations of the two-dimensional flow around a cylinder.
Related Concept Videos
Laminar and Turbulent Flow
Turbulent Flow
Bernoulli's Equation for Flow Along a Streamline
Bernoulli's Equation for Flow Normal to a Streamline
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
Turbulent Flow: Problem Solving
Temperature is a key factor in CO2 solubility. In this case, the CO2 gas and the liquid are cooled to 20°C. Lower temperatures enhance...
Velocity and Acceleration in Steady and Unsteady Flow
The acceleration can be generalized to any point in the flow, and expressed as components along three perpendicular directions, representing changes in velocity over time.

