Traveling Waves in Pipe Flow
Abstract
A family of three-dimensional traveling waves for flow through a pipe of circular cross section is identified. The traveling waves are dominated by pairs of downstream vortices and streaks. They originate in saddle-node bifurcations at Reynolds numbers as low as 1250. All states are immediately unstable. Their dynamical significance is that they provide a skeleton for the formation of a chaotic saddle that can explain the intermittent transition to turbulence and the sensitive dependence on initial conditions in this shear flow.
- Publication:
-
Physical Review Letters
- Pub Date:
- November 2003
- DOI:
- 10.1103/PhysRevLett.91.224502
- arXiv:
- arXiv:nlin/0304029
- Bibcode:
- 2003PhRvL..91v4502F
- Keywords:
-
- 47.20.Ft;
- 47.20.Lz;
- 47.35.+i;
- Instability of shear flows;
- Secondary instabilities;
- Nonlinear Sciences - Chaotic Dynamics;
- Physics - Fluid Dynamics
- E-Print:
- 4 pages, 5 figures