# Nonstationary aspects of passive scalar gradient behaviour

## TL;DR

This study investigates how the orientation and alignment of passive scalar gradients in 2D flows are affected by fluctuating strain persistence, revealing the influence of nonstationary flow dynamics on mixing.

## Contribution

It provides a systematic numerical analysis of passive scalar gradient behavior under fluctuating velocity gradients, highlighting the role of strain persistence fluctuations.

## Key findings

- Gradient orientation is influenced by mean strain persistence when response is weak.
- Statistical alignment depends on the gradient tracking strain persistence fluctuations.
- Unsteady behavior impacts mixing properties in 2D flows.

## Abstract

The dynamics of a passive scalar gradient experiencing fluctuating velocity gradient through the Lagrangian variations of strain persistence is studied. To this end, a systematic, numerical analysis based on the equation for the orientation of the gradient of a non-diffusive scalar in two-dimensional flow is performed. When the gradient responds weakly its orientation properties are determined by the mean value of strain persistence. Statistical alignment of the scalar gradient with the direction defined by the opposed actions of strain and rotation, by contrast, requires the gradient to keep up with strain persistence fluctuations. These results have been obtained for both strain-and effective-rotation-dominated regimes and are supported by relevant experimental data. Consequences of the unsteady behaviour of the scalar gradient on mixing properties are also analyzed.