Pattern Formation Induced by Time-Dependent Advection
Pattern Formation and Solitons
2010-11-15 v1
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.
Cite
@article{arxiv.1011.2910,
title = {Pattern Formation Induced by Time-Dependent Advection},
author = {A. V. Straube and A. Pikovsky},
journal= {arXiv preprint arXiv:1011.2910},
year = {2010}
}