Axial jet in a potentially rotating fluid in a pipe of variable radius

Steady fluid flow in a jet located along the symmetry axis of a potentially rotating flow in a pipe of variable radius is considered. A theoretical model for this flow is constructed. The dependence of the jet parameters on the axial coordinate is investigated in a rigorous formulation under specified entry conditions. In particular, the extensibility or nonextensibility of the solution onto a semi-infinite interval is established. From an analysis of the behavior of the jet, an attempt is undertaken to estimate the behavior of the core of a tornado-like vortex in a pipe of variable radius, namely the possibility of breakdown or jump of the vortex.