Abstracts - KTH Mechanics

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Progress in Reynolds’ problem: transition to turbulence in a
pipe
R.R. Kerswell ∗
The problem of understanding the nature of pressure-driven fluid flow through
a circular straight pipe remains one of the oldest problems in fluid mechanics. At
low flow rates, the realised solution named after Hagen 1 and Poiseuille 2 is steady,
unidirectional and parabolic in profile. For increased level of driving, however, the
flow can easily be triggered into a spatially and temporally disordered 3-dimensional
state 3 . This transition is abrupt, dependent on the level of ambient disturbances in
the system and, at least close to the threshold flow rate, transient. The recent discovery
of travelling wave solutions in this system 4,5 has at last provided a theoretical
stepping stone towards rationalising the transition process. I will discuss these waves,
evidence for their relevance to the transitional dynamics and the current level of our
understanding.
∗ Dept. of Mathematics, University of Bristol, U.K.
1 Hagen, Poggendorfs Annalen def Physik und Chemie 16, 423 (1839)
2 Poiseuille, C.R. Acad. Sci. Paris 11, 961 (1840)
3 Reynolds, Proc. R. Soc. Lond. 35, 84 (1883)
4 Faisst & Eckhardt Phys. Rev. Lett. 91, 22 (2003)
5 Wedin & Kerswell J. Fluid Mech. 508, 333 (2004)
Figure 1: A travelling wave with 4-fold rotational symmetry. On the left, a slice across
the pipe showing fast and slow streaks in the stream velocity (light/dark respectively).
On the right, isocontours of the streamwise vorticity (+/-60% of maximum shown).