  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.
