While standard cosmological models frequently treat the Dark Sector as a non-dissipative background, the morphological duality of the universe—manifesting as spherically symmetric structures (e.g., stellar systems and dark matter halos) versus rotation-dominated vortices (e.g., spiral galaxies and black hole accretion disks)—demands a more comprehensive fluid-dynamical treatment. Building upon the framework of interacting dark fluids and topological stress, this paper investigates the dual mechanical behavior of a viscous Dark Sector. I hypothesize that isotropic volumetric components of the dark fluid act as a global confining pressure, driving the hydrostatic equilibrium necessary for spherical symmetry, while localized shear stresses and angular momentum transfer generate rotational vorticity. By applying continuum mechanics and Navier-Stokes analogies to cosmic scales, I propose a unified morphological framework that explains how distinct stress regimes dictate the geometry of cosmic structures.