A geometric instability of the laminar axisymmetric Euler flows with oscillating flux

TL;DR

This paper demonstrates that highly oscillating inflow-outflow conditions in 3D axisymmetric Euler flows can cause geometric instabilities, preventing the maintenance of smooth laminar profiles when swirl is present.

Contribution

It introduces a new instability mechanism for laminar Euler flows under oscillating flux conditions using geometric analysis techniques.

Findings

Oscillating flux leads to geometric instability in Euler flows.

Laminar profiles cannot remain smooth under high oscillations with swirl.

The analysis employs Frenet-Serret formulas and moving frames.

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 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.