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Science 10 September 2004:
Vol. 305. no. 5690, pp. 1594 - 1598
DOI: 10.1126/science.1100393
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Reports

Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow

Björn Hof,1*{dagger} Casimir W. H. van Doorne,1* Jerry Westerweel,1 Frans T. M. Nieuwstadt,1 Holger Faisst,2 Bruno Eckhardt,2 Hakan Wedin,3 Richard R. Kerswell,3 Fabian Waleffe4

Transition to turbulence in pipe flow is one of the most fundamental and longest-standing problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow rates, but in practice pipe flow becomes turbulent even at moderate speeds. This transition drastically affects the transport efficiency of mass, momentum, and heat. On the basis of the recent discovery of unstable traveling waves in computational studies of the Navier-Stokes equations and ideas from dynamical systems theory, a model for the transition process has been suggested. We report experimental observation of these traveling waves in pipe flow, confirming the proposed transition scenario and suggesting that the dynamics associated with these unstable states may indeed capture the nature of fluid turbulence.

1 Laboratory of Aerodynamics and Hydrodynamics, Delft University of Technology, Leeghwaterstraat 21, 2628 CA Delft, Netherlands.
2 Fachbereich Physik, Philipps-Universität Marburg, 35032 Marburg, Germany.
3 Department of Mathematics, University of Bristol, Bristol, BS8 1TW, UK.
4 Departments of Mathematics and Engineering Physics, University of Wisconsin, Madison, WI 53706, USA.

* These authors contributed equally to this work.

{dagger} To whom correspondence should be addressed. E-mail: b.hof{at}wbmt.tudelft.nl

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Science. ISSN 0036-8075 (print), 1095-9203 (online)