Abstract: Based on the principle of force equilibrium, this study employed the Navier–Stokes equations in cylindrical coordinates (r, θ, z) to derive the three-dimensional spiral vortex velocity fields of mid-latitude cyclones, typhoons, and tornadoes. Singular points (critical points or equilibrium states), at which the three-dimensional velocity of these vortices becomes zero, were identified. All such points were classified as saddle-focus points. Mid-latitude cyclones exhibited two singular points: one at the surface of the Earth and the other at the top of the troposphere. Tornadoes possessed a single singular point at the base of the supercell storm cloud. Typhoons also exhibited two singular points: one at the eyewall surface and the other at the center of the eyewall on the surface. From the derived velocity fields, the horizontal divergence (D), vertical vorticity (ω_z), and vortex shape surface were obtained, and these results were consistent with observational data. The findings indicated that the formation mechanisms of the three spiral vortices differ. Specifically, mid-latitude cyclones are caused by horizontal convergence associated with surface friction and cross-isobar flow, tornadoes are generated by vortex tube stretching resulting from strong horizontal convergence at the base of storm clouds, and typhoons are caused by the large-scale upward motion of the cumulus cloud belt over the ocean, with divergence and convergence remaining invariant with respect to height.