  The dynamics along the particle trajectories for the 3D axisymmetric Euler
equations in an infinite cylinder are considered. It is shown that if the
inflow-outflow is highly oscillating in time, the corresponding Euler flow
cannot keep the uniformly smooth laminar profile provided that the swirling
component is not zero. In the proof, Frenet-Serret formulas and orthonormal
moving frame are essentially used.
