Li's Intrinsic Scale and Equilibrium Transition Theory: Revised Version with Dimensional Consistency and Mathematical Rigor

This paper presents a revised, dimensionally consistent, and mathematically rigorous version of Li’s Intrinsic Scale and Equilibrium Transition Theory for laminar-turbulent transition. The core physical framework remains unchanged: turbulence is not random chaos, but a deterministic small-scale equilibrium state formed when the flow exceeds a critical threshold determined by intrinsic fluid properties. The key revision in this work is the dimensionally consistent definition of Li’s Intrinsic Minimum Length Scale, which corrects the dimensional mismatch in the original formulation while fully preserving the physical meaning: every real fluid has a fixed, inherent minimum length scale determined only by its viscosity and density. This intrinsic scale provides a natural lower bound for flow structures, forbids infinite contraction and singularity formation, and guarantees the global regularity of the incompressible Navier-Stokes equations. The revised theory is logically self-consistent, compatible with classical fluid mechanics, and addresses all major theoretical concerns raised in formal critiques. It still provides a universal, first-principle explanation for the origin, stability, and transition of turbulence.