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