A Simple Passive Scalar Advection-Diffusion Model

TL;DR

This paper introduces a simple one-dimensional passive scalar advection-diffusion model that demonstrates anomalous scaling and explores the dependence of structure function scaling on eddy size, providing insights into turbulence modeling.

Contribution

It offers a straightforward model to test theories of scalar advection and scaling, highlighting the potential non-universality of scaling exponents.

Findings

High order structure function scaling depends on the largest eddy size

Scaling exponents may be geometry-dependent and non-universal

The model serves as a computational test for closure and scaling theories

Abstract

This paper presents a simple, one-dimensional model of a randomly advected passive scalar. The model exhibits anomalous inertial range scaling for the structure functions constructed from scalar differences. The model provides a simple computational test for recent ideas regarding closure and scaling for randomly advected passive scalars. Results suggest that high order structure function scaling depends on the largest velocity eddy size, and hence scaling exponents may be geometry-dependent and non-universal.