Relative periodic orbits in transitional pipe flow
arXiv:0807.2580 · doi:10.1063/1.3009874
Abstract
A dynamical system description of the transition process in shear flows with no linear instability starts with a knowledge of exact coherent solutions, among them travelling waves (TWs) and relative periodic orbits (RPOs). We describe a numerical method to find such solutions in pipe flow and apply it in the vicinity of a Hopf bifurcation from a TW which looks to be especially relevant for transition. The dominant structural feature of the RPO solution is the presence of weakly modulated streaks. This RPO, like the TW from which it bifurcates, sits on the laminar-turbulent boundary separating initial conditions which lead to turbulence from those which immediately relaminarise.
References in corpus (6)
- Turbulence transition and the edge of chaos in pipe flow
- Lower branch coherent states in shear flows: transition and control
- Asymmetric, helical and mirror-symmetric travelling waves in pipe flow
- Reply to Comment on 'Critical behaviour in the relaminarization of localized turbulence in pipe flow'
- Recurrence of Travelling Waves in Transitional Pipe Flow
- Statistical analysis of coherent structures in transitional pipe flow