Turbulent mixing: matching real flows to Kraichnan flows

TL;DR

This paper introduces a method to match real turbulent flows with idealized Kraichnan flows by developing the concept of mixing dimension, revealing inhomogeneity effects and explaining anomalous Lyapunov exponents in compressible turbulence.

Contribution

It proposes a scheme to match real flows to ideal flows using the mixing dimension concept, and models compressible flows to explain observed anomalous Lyapunov exponents.

Findings

Mixing dimension can be fractional and exceeds topological dimension in real flows.

Inhomogeneity of mixing affects reaction rates in turbulence.

A model reproduces observed Lyapunov exponents in compressible flows.

Abstract

Majority of theoretical results regarding turbulent mixing are based on the model of ideal flows with zero correlation time. We discuss the reasons why such results may fail for real flows and develop a scheme which makes it possible to match real flows to ideal flows. In particular we introduce the concept of mixing dimension of flows which can take fractional values. For real incompressible flows, the mixing dimension exceeds the topological dimension; this leads to a local inhomogeneity of mixing --- a phenomenon which is not observed for ideal flows and has profound implications, for instance impacting the rate of bimolecular reactions in turbulent flows. Finally, we build a model of compressible flows which reproduces the anomalous Lyapunov exponent values observed for time-correlated flows by Boffetta et al (2004), and provide a qualitative explanation of this phenomenon.