We introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken experiments carried out with passive tracer particles colored differently. It is shown that the signature for the presence of a chaotic saddle in the advection dynamics is a fractal boundary between regions of different colors. The fractal parts of the boundaries found in the two experiments contain either the stable or the unstable manifold of this chaotic set. We point out that these boundaries coincide with streak lines passing through appropriately chosen points. As an illustrative numerical experiment, we consider a model of the von Kármán vortex street, a time periodic two-dimensional flow of a viscous fluid around a cylinder.
|Number of pages||13|
|Journal||Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics|
|Publication status||Published - 1 May 1995|
- basin boundaries
Péntek, Á., Toroczkai, Z., Tél, T., Grebogi, C., & Yorke, J. A. (1995). Fractal boundaries in open hydrodynamical flows: Signatures of chaotic saddles. Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 51(5), 4076-4088. https://doi.org/10.1103/PhysRevE.51.4076