Energy Dissipation and Stability in the Recursive Splitting Method

A recursive splitting of turbulent regions combined with smooth manifold embedding yields a provably bounded energy framework. Localized energy decays geometrically in each subregion, cross‑region transfers remain uniformly bounded, and curvature constraints prevent finite‑time energy blow‑up. Consequently, global energy conservation and long‑time stability are established under general forcing and boundary conditions.