Filtering the passive scalar transport equation in the large-eddy simulation (LES) of turbulent transport gives rise to the closure term corresponding to the unresolved scalar flux. Understanding and respecting the statistical features of subgrid-scale (SGS) flux is a crucial point in robustness and predictability of the LES. In this work, we investigate the intrinsic nonlocal behavior of the SGS passive scalar flux through studying its two-point statistics obtained from the filtered direct numerical simulation (DNS) data for passive scalar transport in homogeneous isotropic turbulence (HIT). Presence of long-range correlations in true SGS scalar flux urges to go beyond the conventional local closure modeling approaches that fail to predict the non-Gaussian statistical features of turbulent transport in passive scalars. Here, we propose an appropriate statistical model for microscopic SGS motions by taking into account the filtered Boltzmann transport equation (FBTE) for passive scalar. In FBTE, we approximate the filtered equilibrium distribution with an α-stable Lévy distribution that essentially incorporates a power-law behavior to resemble the observed nonlocal statistics of SGS scalar flux. Generic ensemble-averaging of such FBTE lets us formulate a continuum level closure model for the SGS scalar flux appearing in terms of fractional-order Laplacian that is inherently nonlocal. Through a data-driven approach, we infer the optimal version of our SGS model using the high-fidelity data for the two-point correlation function between the SGS scalar flux and filtered scalar gradient, and sparse linear regression. In an a priori test, the optimal fractional-order model yields a promising performance in reproducing the probability distribution function (PDF) of the SGS dissipation of the filtered scalar variance compared to its true PDF obtained from the filtered DNS data.

在湍流输运的大涡模拟 (LES) 中过滤被动标量输运方程会产生对应于未解析标量通量的闭合项。理解和尊重亚网格尺度 (SGS) 通量的统计特征是 LES 稳健性和可预测性的关键点。在这项工作中，我们通过研究从过滤直接数值模拟 (DNS) 数据中获得的 SGS 被动标量通量的两点统计数据，研究了均匀各向同性湍流 (HIT) 中被动标量传输的内在非局域行为。真实 SGS 标量通量中长程相关性的存在促使我们超越传统的局部闭合建模方法，这些方法无法预测被动标量中湍流输运的非高斯统计特征。这里，我们通过考虑被动标量的滤波玻尔兹曼传输方程 (FBTE)，为微观 SGS 运动提出了适当的统计模型。在 FBTE 中，我们将过滤后的平衡分布近似为α -稳定的 Lévy 分布，本质上结合了幂律行为，以类似于观察到的 SGS 标量通量的非局部统计。这种 FBTE 的通用集合平均让我们可以为 SGS 标量通量制定一个连续水平闭合模型，该模型以分数阶拉普拉斯算子出现，本质上是非局部的。通过数据驱动的方法，我们使用 SGS 标量通量和滤波标量梯度之间的两点相关函数的高保真数据以及稀疏线性回归来推断我们的 SGS 模型的最佳版本。在先验 在测试中，最佳分数阶模型在再现过滤标量方差的 SGS 耗散概率分布函数 (PDF) 与从过滤 DNS 数据获得的真实 PDF 相比具有良好的性能。