Europhys. Lett.
Volume 61, Number 5, March 2003
Page(s) 625 - 631
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 01 February 2003
DOI: 10.1209/epl/i2003-00117-6
Europhys. Lett., 61 (5) , pp. 625-631 (2003)

Persistent patterns in deterministic mixing flows

A. Pikovsky and O. Popovych

Department of Physics, University of Potsdam PF 601553, D-14415 Potsdam, Germany

(Received 9 August 2002; accepted in final form 13 December 2002)

We present a theoretical approach to the description of persistent passive scalar patterns observed in recent experiments with non-turbulent time-periodic two-dimensional fluid flows. The behaviour of the passive scalar is described in terms of eigenmodes of the evolution operator which coincides with the Frobenius-Perron operator for the corresponding Lagrangian dynamics with small noise; the latter represents the molecular diffusion. The asymptotic behaviour is dominated by the eigenmode with the slowest decay rate, which is shown to be localized in the non-mixing region of the flow.

47.52.+j - Fluid dynamics: Chaos.
05.40.Jc - Brownian motion.

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