Pattern Formation Induced by Time-Dependent Advection

Details Pattern Formation Induced by Time-Dependent Advection Pattern Formation Induced by Time-Dependent Advection

2010-11-12

arxiv.org/abs/1011.2910v1

Math. Model. Nat. Phenom. Vol. 6, No. 1, 2011, pp. 138-148

Nonlinear Sciences

Pattern Formation and Solitons

Scientific paper

10.1051/mmnp/20116107

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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