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Pattern Formation Induced by Time-DependentAdvection

Published online by Cambridge University Press:  09 June 2010

A. V. Straube and
A. Pikovsky
A. V. Straube*
Affiliation:
Department of Physics, Humboldt University of Berlin, Newtonstr. 15, D-12489, Berlin, GermanyDepartment of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany
A. Pikovsky
Affiliation:
Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany
*
* Corresponding author. E-mail:straube@physik.hu-berlin.de

Abstract

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We study pattern-forming instabilities in reaction-advection-diffusion systems. Wedevelop an approach based on Lyapunov-Bloch exponents to figure out the impact of aspatially periodic mixing flow on the stability of a spatially homogeneous state. We dealwith the flows periodic in space that may have arbitrary time dependence. We propose adiscrete in time model, where reaction, advection, and diffusion act as successiveoperators, and show that a mixing advection can lead to a pattern-forming instability in atwo-component system where only one of the species is advected. Physically, this can beexplained as crossing a threshold of Turing instability due to effective increase of oneof the diffusion constants.

Keywords

pattern formationreaction-advection-diffusion equation

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