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arXiv · 1011.2910

Pattern Formation Induced by Time-Dependent Advection

A. V. Straube·A. Pikovsky
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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.

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A. V. Straube, A. Pikovsky. 2010-11-12. Pattern Formation Induced by Time-Dependent Advection. https://doi.org/10.1051/mmnp%2F20116107

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