Chemical or biological activity in open chaotic flows

Journal Article · Sat May 01 04:00:00 EDT 1999 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.59.5468· OSTI ID:338690

Karolyi, G ^[1]; Pentek, A ^[2]; Toroczkai, Z ^[3]; Toroczkai, Z; Tel, T ^[4]; Grebogi, C ^[5]

---

1. Department of Civil Engineering Mechanics, Technical University of Budapest, Muegyetem rkp. 3, H-1521 Budapest (Hungary)
2. Marine Physical Laboratory, University of California at San Diego, La Jolla, California 92093-0238 (United States)
3. Center for Stochastic Processes in Science and Engineering and Department of Physics, Virginia Polytechnic Institute, Blacksburg, Virgina 24061-0435 (United States)
4. Institute for Theoretical Physics, Eoetvoes University, P.O. Box 32, H-1518 Budapest (Hungary)
5. Institute for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States)

We investigate the evolution of particle ensembles in open chaotic hydrodynamical flows. Active processes of the type A+B{r_arrow}2B and A+B{r_arrow}2C are considered in the limit of weak diffusion. As an illustrative advection dynamics we consider a model of the von K{acute a}rm{acute a}n vortex street, a time-periodic two-dimensional flow of a viscous fluid around a cylinder. We show that a fractal unstable manifold acts as a catalyst for the process, and the products cover fattened-up copies of this manifold. This may account for the observed filamental intensification of activity in environmental flows. The reaction equations valid in the wake are derived either in the form of dissipative maps or differential equations depending on the regime under consideration. They contain terms that are not present in the traditional reaction equations of the same active process: the decay of the products is slower while the productivity is much faster than in homogeneous flows. Both effects appear as a consequence of underlying fractal structures. In the long time limit, the system locks itself in a dynamic equilibrium state synchronized to the flow for both types of reactions. For particles of finite size an emptying transition might also occur leading to no products left in the wake. {copyright} {ital 1999} {ital The American Physical Society}

• OSTI ID: 338690
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 5 Vol. 59; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
ADVECTION
CHEMICAL REACTIONS
DIFFERENTIAL EQUATIONS
FRACTALS
HYDRODYNAMICS
TURBULENCE
VORTEX FLOW
VORTICES