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

TL;DR

This paper investigates an instability mechanism in pulsatile flow along particle trajectories for the 3D axisymmetric Euler equations, showing that rapid inflow-outflow increases can destabilize laminar profiles when swirl is significant.

Contribution

It introduces a new instability mechanism for pulsatile flow in axisymmetric Euler equations, utilizing Frenet-Serret formulas and moving frames to analyze flow stability.

Findings

Rapidly increasing inflow-outflow can destabilize laminar flow profiles.

Instability occurs when the swirling component is not small.

The analysis employs geometric tools like Frenet-Serret formulas.

Abstract

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.