Exact Flat Rotation Curves and Asymptotic Lensing in an Axisymmetric Navier-Stokes Suction Vortex
Year: 2026
Type: preprint
Abstract: We prove that a steady, axisymmetric Navier-Stokes fluid with kinematic viscosity $\nu_A > 0$ surrounding a central sink of radius $R_c$ and inward normal suction speed $v_s > 0$ admits an exact spatially constant azimuthal velocity solution $v_\theta(R) = V_0 = \text{const}$ if and only if the dimensionless suction Reynolds number satisfies $Re_s \equiv v_s R_c / \nu_A = R_c / \delta^* = 1$, where $\delta^* \equiv \nu_A / v_s$ is the Prandtl Asymptotic Suction Boundary Layer (ASBL) displacement thickness. At $Re_s = 1$, the radial viscous stress vanishes identically while the vortex sustains a logarithmic cyclostrophic pressure gradient $\rho^{-1} dP_{\text{vortex}}/dR = V_0^2 / R$ identical to the radial acceleration attributed to an isothermal dark matter halo. Matching this cyclostrophic pressure gradient to the baryonic gravitational acceleration at the core boundary $R_c$ across a background acceleration threshold $a_0$ uniquely locks both $(V_0, R_c)$ to the total baryonic mass via the Baryonic Tully-Fisher relation $V_0^4 = G M_{\text{baryon}} a_0$ and $R_c = \sqrt{G M_{\text{baryon}} / a_0}$. Furthermore, null-geodesic wave refraction across this logarithmic pressure well yields a strictly constant asymptotic bending angle $\Delta\theta_\infty = 2\pi V_0^2 / c_0^2$ independent of impact parameter $b$. Second-order central finite-difference verification matches the analytical flat-rotation solution to $3.21 \times 10^{-12}$, and regularized core integration reproduces observed rotation curves across dwarf and giant spiral galaxies in the SPARC database without dark matter.
Author: Lien, Colt
Institution: University of Arkansas at Monticello
Language: English
Subfield: Astronomy and Astrophysics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225267348