Anomalous Scaling and Refined Similarity of an Active Scalar in a Model of Homogeneous Turbulent Convection

TL;DR

This paper investigates anomalous scaling in active scalar turbulence within homogeneous turbulent convection using a shell model, extending refined similarity concepts and linking intermittency to entropy transfer rate fluctuations.

Contribution

It introduces a novel application of refined similarity ideas to turbulent convection and demonstrates the origin of anomalous scaling through entropy transfer rate variations.

Findings

Conditional scalar and velocity statistics are non-anomalous at fixed entropy transfer rate.

Intermittency corrections are determined by the scaling of entropy transfer rate moments.

The model confirms the hypothesis that entropy transfer rate fluctuations drive anomalous scaling.

Abstract

Anomalous scaling in the statistics of an active scalar in homogeneous turbulent convection is studied using a dynamical shell model. We extend refined similarity ideas for homogeneous and isotropic turbulence to homogeneous turbulent convection and attribute the origin of the anomalous scaling to variations of the entropy transfer rate. We verify the consequences and thus the validity of our hypothesis by showing that the conditional statistics of the active scalar and the velocity at fixed values of entropy transfer rate are not anomalous but have simple scaling with exponents given by dimensional considerations, and that the intermittency corrections are given by the scaling exponents of the moments of the entropy transfer rate.