We introduce the Spatially-Resolved Dynamic Coherence Closure (SDCC), a novel sub-grid scale (SGS) model for large-eddy simulation (LES) of three-dimensional incompressible turbulence. The SDCC couples the Navier-Stokes equations to a local coherence field governed by tailored convection-diffusion-reaction dynamics, which autonomously mediates the eddy viscosity based on local flow topology. In this work, we establish several rigorous mathematical and physical properties of the SDCC model: Strict Invariant Region: We prove that the coherence field operates strictly within the bounded interval (0, 1). This mathematically precludes both non-physical negative viscosity and total dissipation shutdown, entirely eliminating the need for ad hoc clipping. Automatic Transition: Asymptotic analysis demonstrates that the model autonomously recovers Ladyzhenskaya-type damping in high-shear turbulent limits, while strictly vanishing in the laminar limit. This inherently resolves the classical over-dissipation pathology of traditional static models. Global Regularity: We establish global H¹ regularity for the coupled fluid-coherence system. By introducing an advanced spatial transport and gradient control framework, we successfully circumvent the classical supercritical gradient barrier inherent in spatially resolved three-dimensional hydrodynamics. DNS Consistency: The model yields parameter-free statistical predictions that are highly consistent with published direct numerical simulation (DNS) data for high Reynolds number isotropic turbulence. The SDCC framework requires no empirical calibration beyond physically interpretable parameters, offering a mathematically rigorous, numerically stable, and self-calibrating foundation for turbulence modeling.
Hsu et al. (Fri,) studied this question.