Galactic Morphological Resonances: A Fluid-Dynamic Metric for the Hubble Tuning Fork via Vacuum Influx Vortices and Scale-Invariant Dualities

The historical classification of galaxies along the Hubble Tuning Fork separates stellar systems into elliptical, spiral, and barred structures. While standard astrophysics attributes these morphologies to stochastic mergers and complex secular evolution, a definitive, first-principles physical derivation of these geometric boundaries remains elusive. In this paper, we demonstrate that galactic structures are the natural, emergent configurations of a physical, superfluid quantum vacuum executing a systemic inward flow into a central mass-sink. By solving the three-dimensional Navier-Stokes and continuity equations for a rotating fluid influx, we show that galactic shapes represent discrete hydrodynamic standing waves and scale-invariant vortex resonances. We derive the transition from spherical symmetry (elliptical galaxies) to toroidal slip-surfaces and axial polar shafts (spiral galaxies) as a function of the system’s localized angular mass transport. Crucially, we demonstrate a mathematically rigorous, scale-invariant structural duality between galactic morphology and subatomic atomic orbitals, where the galactic bulge, polar jets, and flat stellar disc map identically to the hydrodynamic boundaries of s, p, and d orbitals, respectively.