Statistical Nonlocality of Dynamically Coherent Structures

TL;DR

This paper introduces a stochastic framework for analyzing turbulent transport by modeling flow structures as a Markov process, deriving exact expressions for the transport operator, and connecting to classical diffusivity estimates.

Contribution

It presents a novel stochastic advection model using Markov processes to analyze turbulent transport without approximations.

Findings

Derived closed-form expressions for turbulent transport operator.

Connected the model to classical diffusivity tensor estimates.

Provided a new analytical approach to turbulence analysis.

Abstract

We introduce a class of stochastic advection problems amenable to analysis of turbulent transport. The statistics of the flow field are represented as a continuous time Markov process, a choice that captures the intuitive notion of turbulence as moving from one coherent structure to another. We obtain closed form expressions for the turbulent transport operator without invoking approximations. We recover the classical estimate of turbulent transport as a diffusivity tensor, the components of which are the integrated auto-correlation of the velocity field, in the limit that the operator becomes local in space and time.