Spectral Vorticity Bridge for Turbulent Flows

We introduce a Spectral Vorticity Bridge for incompressible turbulent flow, designed to connect vortex-centered and mode-centered descriptions through a shared operator framework. The bridge has three layers. Layer 1 establishes triad-level transfer identities and sign-structured interaction lemmas in Fourier space. Layer 2 derives band-limited flux bounds that separate direct and inverse transfer regimes under explicit assumptions. Layer 3 defines vortex-coherence spectral diagnostics that can be queried from the same operator object and linked to intermittency proxies.

The goal is a reusable law-level representation: once the spectral operator and projection surfaces are fixed, transfer and cascade observables become repeated linear-algebra and bounded nonlinear queries rather than isolated one-off derivations. We position the framework as a rigorous intermediary between pure geometric vortex narratives and purely statistical spectral scaling narratives.

The paper is a foundational step, not a millennium claim: we do not prove full 3D global regularity. Instead, we provide a theorem-oriented bridge architecture intended to support future regularity criteria, intermittency analysis, and physically interpretable turbulence diagnostics across simulation and reduced-order settings.