A Sakin–Mutaharrik Hydrodynamic Vortex Model for Galactic Rotation Curves Across Dwarf to Giant Galaxies Without Dark Matter Particles

The flat rotation curves of spiral and dwarf galaxies represent one of the most persistent unsolved problems in modern astrophysics. Standard LCDM cosmology attributes the discrepancy between luminous baryonic matter and observed stellar velocities to hypothetical non-baryonic Dark Matter particles, which have eluded direct laboratory detection for over four decades. In this paper, we propose a novel, parameter-locked hydrodynamic model—the Sakin–Mutaharrik Cosmic Fluid Vortex Model—inspired by classical cosmological fluid descriptions preserved in Nahj al-Balagha (Sermons 1 and 91). Instead of treating interstellar space as an empty vacuum populated by collisionless dark matter particles, we model the cosmic medium as an inviscid, wave-bearing fluid governed by four coupled physical mechanisms: (1) a stationary background wave pressure (Al-Sakin), (2) an enclosed-mass coupled moving wave (Al-Mutaharrik), (3) Bernoulli-like rotational energy conservation from core vortex churning (Al-Makhd), and (4) gravitational mass-saturation anchoring (Al-Kabs) gated by a Froude/Mach-scaled 2D vortex core (Lujjat Tayyar). Using only three universal fluid constants calibrated on three benchmark spiral galaxies, we perform a zero-tuning blind test across five unseen galaxies spanning an extreme dynamical range from 47 km/s (dwarf galaxy DDO 154) to 315 km/s (giant spiral NGC 2841), including the Milky Way. The locked universal equation achieves an average accuracy of 98.10% across unseen spiral galaxies (98.78% on the Milky Way, RMSE = 2.8 km/s) and 95.89% across all eight diverse galaxies without invoking dark matter particles.Corresponding Author: Jafar Husain | Contact Email: jh88680@gmail.com