Lagrangian model for passive scalar gradients in turbulence

TL;DR

This paper develops a Lagrangian model for passive scalar gradients in turbulence, extending a recent Gaussian field closure approach, and improves its accuracy by incorporating trajectory history information, achieving good agreement with DNS data up to moderate Reynolds numbers.

Contribution

It introduces a novel Lagrangian scalar gradient model based on RDGF closure, enhanced with trajectory history data, for better turbulence scalar predictions.

Findings

Model accurately predicts scalar gradients and alignments with strain eigenvectors.

Incorporating trajectory history improves model accuracy significantly.

Model's validity extends up to Reynolds number approximately 500.

Abstract

The equation for the fluid velocity gradient along a Lagrangian trajectory immediately follows from the Navier-Stokes equation. However, such an equation involves two terms that cannot be determined from the velocity gradient along the chosen Lagrangian path: the pressure Hessian and the viscous Laplacian. A recent model handles these unclosed terms using a multi-level version of the recent deformation of Gaussian fields (RDGF) closure (Johnson \& Meneveau, Phys.~Rev.~Fluids, 2017). This model is in remarkable agreement with DNS data and works for arbitrary Taylor Reynolds numbers $\Rey_\lambda$. Inspired by this, we develop a Lagrangian model for passive scalar gradients in isotropic turbulence. The equation for passive scalar gradients also involves an unclosed term in the Lagrangian frame, namely the scalar gradient diffusion term, which we model using the RDGF approach. However, comparisons of the statistics obtained from this model with direct numerical simulation (DNS) data reveal substantial errors due to erroneously large fluctuations generated by the model. We address this defect by incorporating into the closure approximation information regarding the scalar gradient production along the local trajectory history of the particle. This modified model makes predictions for the scalar gradients, their production rates, and alignments with the strain-rate eigenvectors that are in very good agreement with DNS data. However, while the model yields valid predictions up to around $\Rey_\lambda\approx 500$, beyond this, the model breaks down.