Tempered Fractional LES Modeling

Abstract

The presence of nonlocal interactions and intermittent signals in the homogeneous isotropic turbulence grant multi-point statistical functions a key role in formulating a new generation of large-eddy simulation (LES) models of higher fidelity. We establish a tempered fractional-order modeling framework for developing nonlocal LES subgrid-scale models, starting from the kinetic transport. We employ a tempered L\'evy-stable distribution to represent the source of turbulent effects at the kinetic level, and we rigorously show that the corresponding turbulence closure term emerges as the tempered fractional Laplacian, $(\Delta+\lambda)^{\alpha} (\cdot)$, for $\alpha \in (0,1)$, $\alpha \neq \frac{1}{2}$, and $\lambda>0$ in the filtered Navier-Stokes equations. Moreover, we prove the frame invariant properties of the proposed model, complying with the subgrid-scale stresses. To characterize the optimum values of model parameters and infer the enhanced efficiency of the tempered fractional subgrid-scale model, we develop a robust algorithm, involving two-point structure functions and conventional correlation coefficients. In an a priori statistical study, we evaluate the capabilities of the developed model in fulfilling the closed essential requirements, obtained for a weaker sense of the ideal LES model (Meneveau 1994). Finally, the model undergoes the a posteriori analysis to ensure the numerical stability and pragmatic efficiency of the model.