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The equation for the fluid velocity gradient along a Lagrangian trajectoryimmediately follows from the Navier-Stokes equation. However, such an equationinvolves two terms that cannot be determined from the velocity gradient alongthe chosen Lagrangian path: the pressure Hessian and the viscous Laplacian. Arecent model handles these unclosed terms using a multi-level version of therecent deformation of Gaussian fields (RDGF) closure (Johnson \& Meneveau,Phys.~Rev.~Fluids, 2017). This model is in remarkable agreement with DNS dataand works for arbitrary Taylor Reynolds numbers $\Rey_\lambda$. Inspired bythis, we develop a Lagrangian model for passive scalar gradients in isotropicturbulence. The equation for passive scalar gradients also involves an unclosedterm in the Lagrangian frame, namely the scalar gradient diffusion term, whichwe model using the RDGF approach. However, comparisons of the statisticsobtained from this model with direct numerical simulation (DNS) data revealsubstantial errors due to erroneously large fluctuations generated by themodel. We address this defect by incorporating into the closure approximationinformation regarding the scalar gradient production along the local trajectoryhistory of the particle. This modified model makes predictions for the scalargradients, their production rates, and alignments with the strain-rateeigenvectors that are in very good agreement with DNS data. However, while themodel yields valid predictions up to around $\Rey_\lambda\approx 500$, beyondthis, the model breaks down.

Lagrangian model for passive scalar gradients in turbulence