Statistical field theory for a passive vector model with spatially linear advection

TL;DR

This paper develops a statistical field theory for a passive vector turbulence model with spatially linear advection, capturing non-Gaussian intermittency features through a Hopf functional approach and numerical analysis.

Contribution

It introduces a novel statistical framework for a passive vector turbulence model, utilizing Hopf formalism to decompose complex non-Gaussian statistics into Gaussian sub-ensembles.

Findings

Model exhibits non-Gaussian, intermittent energy flux characteristic of turbulence.

Hopf formalism enables decomposition of complex statistics into simpler Gaussian components.

Numerical implementation effectively characterizes intermittency in the model.

Abstract

One challenge in developing a statistical field theory of turbulence is the analysis of the functional equations that govern the complete statistics of the flow field. Simplified models of turbulence may help to develop such a statistical framework. Here, we consider the advection and stretching of an incompressible passive vector field by a spatially linear stochastic field as a model for small-scale turbulence. The model encompasses non-Gaussian statistics due to an intermittent energy flux from large scales to small scales, thereby displaying hallmark features of turbulence. We explore this model using the Hopf functional formalism, which naturally leads to a decomposition of the complex non-Gaussian statistics into Gaussian sub-ensembles based on different realizations of the advecting field. We then characterize intermittency of the model using a numerical implementation, which takes advantage of this statistical decomposition.