Hessian-based Lagrangian closure theory for passive scalar turbulence

TL;DR

This paper introduces a Hessian-based closure theory for passive scalar turbulence that captures key features like scale-locality and conservation, successfully deriving the Obukhov-Corrsin spectrum consistent with empirical data.

Contribution

It presents a novel closure model using the Hessian of the scalar field, incorporating realistic features and deriving the universal spectrum in the inertial-convective range.

Findings

Derivation of the Obukhov-Corrsin spectrum with a universal constant

Model captures scale-locality and conservation in scalar turbulence

Results align with numerical and experimental data

Abstract

Self-consistent closure theory for passive-scalar turbulence has been developed on the basis of the Hessian of the scalar field. As a primitive indicator of spatial structure of the scalar, we employ the Hessian into the core of the theory to properly characterize the time scale intrinsic to the scalar field itself. The resultant closure model is now endowed with several realistic features, i.e. the scale-locality of the interscale interaction, the detailed conservation, and the memory-fading effect. Applying the current theory to the inertial-convective range eventually leads to self-consistent derivation of the Obukhov-Corrsin spectrum with its universal constant consistent with numerical and experimental data.