Geometry of stratified turbulent mixing: local alignment of the density gradient with rotation, shear and viscous dissipation

TL;DR

This paper presents a geometric framework for analyzing turbulent mixing in stratified flows, revealing how density gradients align with rotation, shear, and dissipation, providing new insights into diapycnal mixing mechanisms.

Contribution

It introduces a novel geometric analysis based on local bases from the velocity gradient tensor to study density gradient alignment in stratified turbulence.

Findings

Density gradients align with minimum dissipation directions in high shear regions.

Gradients tend to be normal to the plane of rotex and shear vectors.

The framework offers new insights into the relationship between density gradients and dissipation.

Abstract

We introduce a geometric analysis of turbulent mixing in density-stratified flows based on the alignment of the density gradient in two orthogonal bases that are locally constructed from the velocity gradient tensor. The first basis connects diapycnal mixing to rotation and shearing motions, building on the recent 'rortex-shear decomposition' in stratified shear layers (Jiang et al., J. Fluid Mech. 947, A30, 2022), while the second basis connects mixing to the principal axes of the viscous dissipation tensor. Applying this framework to datasets taken in the stratified inclined duct laboratory experiment reveals that density gradients in locations of high shear tend to align preferentially (i) along the direction of minimum dissipation and (ii) normal to the plane spanned by the rotex and shear vectors. The analysis of the local alignment across increasingly turbulent flows offers new insights into the intricate relationship between the density gradient and dissipation, and thus diapycnal mixing.