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Pattern Formation Induced by Time-Dependent Advection

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, Germany Department 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
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Abstract

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

Keywords

pattern formationreaction-advection-diffusion equation
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 1: Instability and patterns. Issue dedicated to the memory of A. Golovin , 2011 , pp. 138 - 148
Copyright
© EDP Sciences, 2010

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