Geodesic
Pattern Formation Induced by Time-Dependent Advection
A. V. Straube1, 2 ; A. Pikovsky2
1 Department of Physics, Humboldt University of Berlin, Newtonstr. 15, D-12489, Berlin, Germany
2 Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany
Mathematical modelling of natural phenomena, Tome 6 (2011) no. 1, pp. 138-148.

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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.
DOI : 10.1051/mmnp/20116107

A. V. Straube 1, 2 ; A. Pikovsky 2

1 Department of Physics, Humboldt University of Berlin, Newtonstr. 15, D-12489, Berlin, Germany
2 Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam-Golm, Germany 
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A. V. Straube; A. Pikovsky. Pattern Formation Induced by Time-Dependent Advection. Mathematical modelling of natural phenomena, Tome 6 (2011) no. 1, pp. 138-148. doi : 10.1051/mmnp/20116107. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20116107/

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