An instability mechanism of pulsatile flow along particle trajectories for the axisymmetric Euler equations

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 rapidly increasing in time, the corresponding laminar profile of the Euler flow is not (in some sense) stable provided that the swirling component is not small. This exhibits an instability mechanism of pulsatile flow. In the proof, Frenet-Serret formulas and orthonormal moving frame are essentially used.