How can simple fluid flows produce chaotic motion? In this project, we explore how passive particles move in the wake of a cylinder placed in a flowing fluid — a classic setup that surprisingly leads to rich and chaotic dynamics. When vortices form behind the obstacle, particles can become temporarily trapped, following unpredictable paths before eventually escaping.

Using numerical simulations of fluid flow as well as analytical model systems, we apply ideas from chaotic scattering theory to uncover hidden structures in the flow. Concepts such as periodic orbits, streaklines, Lyapunov exponents, and escape rates are used to reveal the geometry and dynamics of chaos in an open hydrodynamical system.

This project combines fluid dynamics, nonlinear dynamics, and computational physics, and offers hands-on experience with simulations and data analysis. It is ideal for students interested in chaos, pattern formation, and the unexpected complexity that can arise in seemingly simple physical systems.

Initial references:
[1] – Jung, C., Tél, T., & Ziemniak, E. (1993). Application of scattering chaos to particle transport in a hydrodynamical flow. Chaos: An Interdisciplinary Journal of Nonlinear Science, 3(4), 555-568.
[2] – Ziemniak, E. M., Jung, C., & Tél, T. (1994). Tracer dynamics in open hydrodynamical flows as chaotic scattering. Physica D: Nonlinear Phenomena, 76(1-3), 123-146.