Mixing-induced activity in open flows

TL;DR

This paper presents a theoretical framework for understanding how local mixing in open flows can induce a transition from convective to absolute instability in active fields, with universal scaling laws validated by simulations.

Contribution

It introduces an analytical model linking local mixing to global instability transition and derives a universal critical exponent for weakly nonlinear regimes.

Findings

Derived the linear transition point analytically

Established a universal scaling law for instability growth

Validated theory with numerical simulations

Abstract

We develop a theory describing how a convectively unstable active field in an open flow is transformed into absolutely unstable by local mixing. Presenting the mixing region as one with a locally enhanced effective diffusion allows us to find the linear transition point to an unstable global mode analytically. We derive the critical exponent that characterizes weakly nonlinear regimes beyond the instability threshold and compare it with numerical simulations of a full two-dimensional flow problem. The obtained scaling law turns out to be universal as it depends neither on geometry nor on the nature of the mixing region.