A Hydrodynamic Approach to Macroscopic Gravity: Thermodynamic Equilibrium via Viscous Dissipation and Quaternion Tensors [JSK Research Part 1, v1.2]

This paper presents a novel hydrodynamic framework for macroscopic gravity, bridging the gap between Einstein's tensor geometry and Navier-Stokes fluid dynamics. By modeling the gravitational field as a continuous flow of Vacuum Fluctuation Energy, a quaternion tensor is introduced to resolve the topological coordinate singularity (gimbal lock phenomenon) inherent in rotating celestial bodies. Furthermore, to prevent the non-physical gravitational collapse observed in conventional mass-density singularity models, a hydrostatic pressure gradient is coupled with a radial density stratification function. This system reaches a permanent thermodynamic equilibrium state by suppressing the exponential divergence of turbulent kinetic energy (TKE) through a kinematic viscous dissipation term. This hydrodynamic formulation successfully eliminates infinite density singularities without relying on the constraints of quantum gravity, providing a computable macroscopic field theory for planetary geometry.