Turbulence Admissibility: Constraint Compatibility in Turbulent Fluid Systems

This paper introduces the concept of turbulence admissibility within the Paton System framework. Traditional descriptions of turbulence interpret turbulent flow as chaotic behaviour emerging from nonlinear interactions within the Navier–Stokes equations. However, even highly irregular turbulent systems remain governed by strict physical constraints including conservation of mass, momentum, and energy. The Paton System interprets turbulent motion as admissible trajectories within a constrained dynamical manifold defined by governing physical laws. Turbulence therefore represents complex but structurally valid continuation of fluid states within the admissible region of the system. By identifying turbulence as admissible continuation within constraint-defined phase space, this framework clarifies why turbulent behaviour remains bounded despite its apparent complexity. This work represents a Tier-7 domain instantiation of the Paton System within physical systems, applying the admissibility framework to turbulent fluid dynamics and linking turbulence to the broader structural theory of admissible system evolution.