Coherence Geometry as a Structured Generalization of Fluid Dynamics

This paper develops a coherence-geometric generalization of fluid dynamics in which observable motion arises from structured phase and amplitude fields rather than being introduced only at the level of a macroscopic velocity field. The construction incorporates potential and rotational phase channels, amplitude-localized transport, non-local pressure projection, diffusion and hyper-viscosity, torsional coupling, and internal coherence response. The work develops analytical correspondences with major structures appearing in Navier–Stokes dynamics while exploring a deeper Source-level geometry from which transport, rotation, pressure regulation, dissipation, and persistent vortical organization may arise. Numerical experiments investigate interacting vortices, spiral and filamentary structures, amplitude-dependent flow, and vortex-shedding-like behavior. Supporting Jupyter notebooks preserving several of these computational investigations are included with the archival record. The paper is intended as a constructive exploration of an underlying coherence-geometric substrate for fluid-like dynamics, placing familiar fluid structures within a broader Source-geometric framework.CGI Internal ID: CGI-RSR-000041