Large spiral and target waves: Turbulent diffusion boosts scales of pattern formation

TL;DR

This study provides the first experimental evidence that turbulent diffusion significantly enlarges the scale of reaction-diffusion patterns like spiral and target waves, confirming that their speed scales with the square root of turbulent diffusion.

Contribution

It demonstrates experimentally that turbulent flow can boost pattern scales in reaction-diffusion systems and confirms the FKPP wave speed relation under turbulent conditions.

Findings

Target and spiral wave patterns are ~50 times larger with turbulence.

Wave speed scales with the square root of turbulent diffusion D_*.

Wavefronts are highly filamentous, deviating from molecular diffusion expectations.

Abstract

In absence of advection, reaction-diffusion systems are able to organize into spatiotemporal patterns, in particular spiral and target waves. Whenever advection is present and can be parameterised in terms of effective or turbulent diffusion $D_{*}$, these patterns should be attainable on much greater, boosted lengthscale. However, so far, experimental evidence of these boosted patterns in turbulent flow was lacking. Here, we report the first experimental observation of boosted target and spiral patterns in an excitable chemical reaction in a quasi two-dimensional turbulent flow. The wave patterns observed are $\sim 50$ times larger than in the case of molecular diffusion only. We vary the turbulent diffusion coefficient $D_{*}$ of the flow and find that the fundamental Fisher-Kolmogorov-Petrovsky-Piskunov (FKPP) equation $v_{f} \propto \sqrt{D_{*}}$ for the asymptotic speed of a reactive wave remains valid. However, not all measures of the boosted wave scale with $D_{*}$ as expected from molecular diffusion, since the wavefronts turn out to be highly filamentous.