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Pattern formation induced by time-dependent advection

  • 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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Author:Arthur V. Straube, Arkady S. PikovskyORCiDGND
Parent Title (English):Postprints der Universität Potsdam : Mathematisch Naturwissenschaftliche Reihe
Series (Serial Number):Postprints der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe (575)
Document Type:Postprint
Date of first Publication:2019/02/05
Year of Completion:2011
Publishing Institution:Universität Potsdam
Release Date:2019/02/06
Tag:pattern formation; reaction-advection-diffusion equation
First Page:138-147
Source:Mathematical modelling of natural phenomena 6 (2011) 1, pp. 138–147 DOI 10.1051/mmnp/20116107
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Peer Review:Referiert
Publication Way:Open Access
Grantor:Cambridge University Press (CUP)
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht