Abstract:

We establish that two-dimensional turbulence emerges from parabolic geometric foundations rather than being constrained by topological laws. The relations n² = m and j² = k generate both discrete vortex quantization and continuous topological invariants through the closure operator ξ.

This resolves the apparent stochasticity of turbulence as deterministic evolution in parabolic coordinates, with Gauss-Bonnet constraints emerging as statistical aggregates of quantum vortex structure.