Localized turbulent structures in a circular pipe

Transition to turbulence in a pipe flow begins with the appearance of spatially localized structures, such as turbulent puffs. The investigation of a conditionally time-periodic solution of the Navier–Stokes equations, which is qualitatively close to a turbulent puff, is carried out with the aim to explain the mechanism of turbulent puffs. Such solutions are given by the separatrix dividing the attraction regions of laminar and turbulent solutions. In particular, it is shown that the mechanism underlying oscillations is not driven by the Kelvin–Helmholtz instability, which was considered as the main mechanism of oscillation generation in the turbulent puff.