Pattern Formation Induced by Time-Dependent Advection

TL;DR

This paper investigates how time-dependent, spatially periodic advection influences pattern formation in reaction-diffusion systems, revealing that mixing flows can induce Turing-like instabilities even with selective advection.

Contribution

It introduces a Lyapunov-Bloch exponent approach and a discrete-time model to analyze the impact of periodic advection on pattern stability in reaction-diffusion systems.

Findings

Mixing advection can induce pattern-forming instabilities.

A two-component system with selective advection can cross Turing thresholds.

The effective increase of diffusion constants explains the instability mechanism.

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.