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In this study, we revisit the spectral transfer model for the turbulentintensity in the passive scalar transport (under large-scale anisotropicforcing), and a subsequent modification to the scaling of scalar variancecascade is presented. From the modified spectral transfer model, we obtain arevised scalar transport model using fractional-order Laplacian operator thatfacilitates the robust inclusion of the nonlocal effects originated fromlarge-scale anisotropy transferred across the multitude of scales in theturbulent cascade. We provide an $\textit{a priori}$ estimate for the nonlocalmodel based on the scaling analysis of scalar spectrum, and later examine ourdeveloped model through direct numerical simulation. We present a detailedanalysis on the evolution of the scalar variance, high-order statistics ofscalar gradient, and important two-point statistical metrics of the turbulenttransport to make a comprehensive comparison between the nonlocal model and itsstandard version. Finally, we present an analysis that seamlessly reconcilesthe similarities between the developed model with the fractional-ordersubgrid-scale scalar flux model for the large-eddy simulation (Akhavan-Safaeiet al. 2021) when the filter scale approaches the dissipative scales ofturbulent transport. In order to perform this task, we employ a Gaussianprocess regression model to predict the model coefficient for thefractional-order subgrid model.

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