Li's Intrinsic Scale and Equilibrium Transition Theory: A Universal Mechanism for Fluid Stability and Turbulence Transition

This paper establishes a complete, mathematically rigorous, and physically consistent theory of fluid dynamics and laminar-turbulent transition, named Li’s Intrinsic Scale and Equilibrium Transition Theory. The core contribution of this work is to reveal that turbulence is not stochastic chaos, but a deterministic, structured equilibrium state at a smaller spatial scale, which emerges when the flow exceeds a critical threshold determined by intrinsic fluid properties. Every real fluid possesses a fixed, positive intrinsic minimum length scale determined solely by its kinematic viscosity (ν) and mass density (ρ). This scale acts as a natural lower bound for all coherent flow structures, preventing infinite contraction, singularity formation, and finite-time blowup in the Navier-Stokes equations. When external forcing exceeds the critical stability threshold, the original large-scale laminar structure breaks down and reorganizes into a new dynamic equilibrium at a smaller scale, which corresponds to the physical phenomenon known as turbulence. The theory is fully consistent with the incompressible Navier-Stokes equations, classical energy dissipation laws, and all experimentally verified results in fluid mechanics. It provides a unified explanatory framework for flow transition, energy transfer, and flow stability, with direct, verifiable applications in aerospace engineering, cardiovascular hemodynamics, pipeline transport, and meteorological dynamics. Unlike traditional statistical or chaotic models, this theory offers deterministic predictability and physical interpretability, enabling systematic design and control of fluid systems.