A fluid swirling through an axisymmetrically deformed tube is considered, ignoring viscosity and compressibility. For a tube of radius R, having a longitudinal wall deformation of wave number k, the flow near the wall is blocked, if the Rossby number assumes one of the critical values (λ2n + k2R2)−½, where n is any positive integer, and λn is the nth zero of the Bessel function J1(λ). Rossby number is defined as W/2Rω, in which W and ω are the uniform axial and angular velocities in an undeformed tube. For a convergent-divergent nozzle, the critical Rossby numbers have the same form, with kR = 0. The flow exhibits radically different patterns when each critical Rossby number is crossed.