The Navier‐Stokes equations for incompressible rotationally symmetric vortex flow at high swirl and large core Reynolds number are shown to approximate to the equation of inviscid rotating flow in regions where axial gradients are large. This equation becomes linear for flow originally near the axis, where rigid rotation results from viscous action. Series solutions at high supercritical swirl values near the critical one under the condition of flow retardation near the axis are found to exhibit the experimentally observed features of vortex breakdown flows: bulges of decelerated flow, or bubbles of recirculating fluid, with reversed axial and swirl velocities near the axis. It is concluded that the vortex breakdown in vortex tubes and on delta wings is neither due to hydrodynamic instability, nor is it a phenomenon akin to the hydraulic jump. Rather it is a regular feature of the solution of the equations of motion under the given conditions.