A Nonlocal Spectral Transfer Model and New Scaling Law for Scalar Turbulence

Abstract: In this study, we revisit the spectral transfer model for the turbulent intensity in the passive scalar transport (under large-scale anisotropic forcing), and a subsequent modification to the scaling of scalar variance cascade is presented. From the modified spectral transfer model, we obtain a revised scalar transport model using fractional-order Laplacian operator that facilitates the robust inclusion of the nonlocal effects originated from large-scale anisotropy transferred across the multitude of scales in the turbulent cascade. We provide an $\textit{a priori}$ estimate for the nonlocal model based on the scaling analysis of scalar spectrum, and later examine our developed model through direct numerical simulation. We present a detailed analysis on the evolution of the scalar variance, high-order statistics of scalar gradient, and important two-point statistical metrics of the turbulent transport to make a comprehensive comparison between the nonlocal model and its standard version. Finally, we present an analysis that seamlessly reconciles the similarities between the developed model with the fractional-order subgrid-scale scalar flux model for the large-eddy simulation (Akhavan-Safaei et al. 2021) when the filter scale approaches the dissipative scales of turbulent transport. In order to perform this task, we employ a Gaussian process regression model to predict the model coefficient for the fractional-order subgrid model.