Turbulent Cylinder Flow as Sphere-Torus Topological Phase Transitions

Karman vortex street formation behind circular cylinders is explained through sphere-torus topological phase transitions. The continuous transverse pressure wave corresponds to spherical phase oscillations (S2), while discrete vortices emerge as toroidal phase defects (T 2). Separation points act as topological transition zones where Reynolds number triggers S2 ↔ T 2 conversions. The Strouhal number St ≈ 0.2 emerges as a topological invariant, resolving the wave-vortex duality in turbulence. Experimental predictionsinclude resonant shedding enhancement at ωres and topological drag reduction proportional to curvature integral.