Lagrangian Model for Passive Scalar Gradients in Turbulence

The equation for the fluid velocity gradient along a Lagrangian trajectory can be derived from the Navier-Stokes equation, but it involves two terms that cannot be determined from the velocity gradient along the chosen trajectory, namely the pressure Hessian and the viscous term. Building on a number of previous works, a recent model has been derived that handles these terms using a multiscale, recent deformation of Gaussian fields (MRDGF) closure (Johnson & Meneveau, Phys. Rev. Fluids, 2017). This model has been shown to describe DNS data very accurately and it works for arbitrary Reynolds numbers, unlike previous models that were restricted to relatively low Reynolds numbers. Here we extend the model to the case of a passive scalar gradient, using the MRDGF closure to handle the scalar dissipation term, and also consider how the model can capture the effect of the scalar Schmidt number. Predictions from the model are compared with those from DNS, and extensions of the model to stably stratified turbulent flows will be discussed.