Multilevel Lagrangian model for passive scalar gradients in turbulence at high Reynolds and Schmidt numbers

Zhang et al. (J. Fluid Mech., 964, A39, 2023) formulated a model for the Lagrangian evolution of passive scalar gradients in isotropic turbulence in which the diffusion term in the equation was closed using the recent deformation of Gaussian fields (RDGF) approach. The velocity gradient appears in the scalar gradient equation, and this was specified using the model of Johnson & Meneveau (Phys. Rev. Fluids, vol. 2 (7), 2017, 072601), which is based on a multi-level recent deformation of Gaussian fields (ML-RDGF) closure, enabling predictions at arbitrary Taylor Reynolds numbers Re_λ. The predictions from the model of Zhang et al. are in very good agreement with DNS data over the range Re_λ ≤ 250. However, the model blows up when Re_λ ≥ 500, and at lower Re_λ when the Schmidt number Sc is larger than one. To address these issues, we extend the Zhang et al. model to utilize the full ML-RDGF closure approach for the scalar gradient diffusion term, but with a recent deformation timescale based on the scalar gradient dynamics. This closure also enables the scalar gradient model to make robust predictions in the regime Sc>1, where there is a difference in the scale at which the largest velocity and scalar gradients exist.