The Peridynamic Differential Operator (PDDO) provides a nonlocal numerical framework that has shown promising performance in weakly compressible fluid simulations, particularly for low-Reynolds-number laminar flows. However, extending PDDO-based methods to high-Reynolds-number turbulent flows remains challenging due to multiscale interactions and stringent requirements on numerical stability and spatial resolution. These limitations have hindered the direct application of existing PDDO discretizations to practical turbulent flow problems. In this study, a novel Eulerian PDDO framework coupled with Large Eddy Simulation (LES) is developed to enable turbulence simulations across a wide range of Reynolds numbers. Within the LES framework, a Gaussian filter is applied to the weakly compressible Navier–Stokes equations, and a scale decomposition is performed to derive the governing equations incorporating subgrid-scale (SGS) stresses. Exploiting the intrinsic nonlocal characteristics of peridynamics, the SGS closure terms, including the turbulent eddy viscosity, are reformulated into consistent nonlocal integral representations using PDDO. This nonlocal SGS modeling strategy preserves essential multiscale interactions that are often weakened in conventional turbulence models based on local differential operators. The proposed approach is validated using two-dimensional channel flow and flow past a circular cylinder over a broad range of Reynolds numbers. Numerical results are compared with commercial CFD simulations and available experimental data. The results indicate that the predictions obtained by the proposed method are in good agreement with both commercial CFD software and experimental observations. The present work highlights the potential of peridynamics-based nonlocal numerical methods for high-fidelity turbulent flow simulations and provides a robust computational framework for extending PDDO applications to complex, high-Reynolds-number flow regimes.