Turbulence has finite lifespan
At a low speed fluid or gas flows evenly in a tube (called 'laminar' in technical jargon). The flow becomes turbulent beyond a certain speed. For over a century researchers have been trying to understand how the transition changes, but up to now they still do not know. Researchers at Delft University of Technology and Phillips-Universität Marburg have recently discovered that a turbulent perturbation in a tube will always become a laminar flow if you just wait long enough. Obviously, turbulence is merely a transient state in a laminar flowing medium. This is a significant new clue in the search of understanding the connection between laminar flows and turbulent ones. The researchers have their results published in Nature of 7 September 2006.
Anybody who opens a tap may see that the jet of water is even at first. This is called laminar flow. If the tap is opened further, the jet of water becomes uneven at a certain point by turbulence in the water supply. This turbulence causes an increasing of the resistance: it needs more power to pump the fluid through the tube. For industrial applications it proves to be helpful that the resistance is as low as possible, for example, air that flows alongside the wings of an aeroplane, or oil that is being pumped through long pipelines.
From laminar to turbulent
Every science student is being taught that a flow in a tube will turn from laminar to turbulent at a critical Reynolds number between 2000 and 2300. This dimensionless number is highly important in hydrodynamics. It is a standard for the ratio between the rate of flow and the friction of the fluid.
People try to understand the origin of turbulence by developing small perturbations on a laminar state. Already in 1883 Osborne Reynolds proved that (small) perturbations always decay. A mathematical analysis of stability of the kinetic equations do show that there is only one stable solution, namely the laminar state. In practice, however, it is shown that turbulence may be maintained in a pipe flow. Scientists have been keeping busy by this mystery for over a century.
Alternative solutions
How is it possible that turbulence can exist if, mathematically, only one state is possible, namely a laminar flow? Some years ago theoreticians discovered new, exact solutions of the kinetic equations for a fluid in a tube, the so-called 'travelling waves'. These solutions are unstable and so, they are not able to exist permanently. In 2004 researchers noticed the solutions by experiment for the first time. Then it became clear that the travelling waves had to play a part in explaining turbulence1).. The following scenario has developed: at a sufficiently large perturbation of a laminar flow, a travelling wave may arise. A travelling wave is unstable and consequently, is not only able to fall back to a laminar state, or to a different travelling wave again. Researchers discovered from large-scale simulations that the lifespan of the perturbation in the surrounding area of the travelling waves, increases at the Reynolds number. The simulations are affirming that the lifespan of the perturbation becomes infinite beyond the critical Reynolds number. This would account for the permanent state of turbulence.
To affirm theory by experiment
Researchers2) from universities at Delft, Manchester and Marburg wanted to affirm the scenario by experiment. They set up a construction consisting of a pipe with a length of 7500 times its diametre (viz. most of the laboratory constructions have only a pipe length between 500 and 800 times its diametre). Thereupon, the researchers introduced perturbations in the pipe and searched whether the perturbations did not fade away anymore when increasing the Reynolds number. Remarkably, it appeared that perturbations do always fade away. They deduced that the lifespan of turbulent perturbations become only infinite at an infinite high Reynolds number and not at a finite value between 2000 and 2300. The observations seem also to apply to the behaviour of turbulent perturbations in different types of flows.
Fading turbulence
With this research the hypothesis has been rejected that turbulence exists as a permanent state beyond a Reynolds number: a turbulent perturbation will always fade away if you just wait for a sufficient long time. The lifespan of turbulent perturbations strongly increases at the Reynolds number. By extrapolating their results the researchers expect that a turbulent perturbation in a pipe of one centimetre across, say a garden hose, and at a Reynolds number of 2400, will fade away after about five years. In this period the perturbation has travelled a distance of 40,000 kilometres, i.e. the circumference of the earth. Similar time scales and distances are less relevant to industrial applications, but they might be important in astrophysics (for example, at the formation of planets around stars) that has gigantic longer time scales.
Now that has been proven that turbulence is not a permanent state, it should be possible to manipulate turbulent perturbations in such a way that the flow of a turbulent state (at a high resistance) can be brought into a laminar state (lower resistance). This could provide an interesting perspective in suppressing turbulence and decreasing hydrodynamic resistance for industrial applications.
1) see also Hof et al., Science 305 (2004) 1594 and Golven in turbulente buisstromingen experimenteel aangetoond.
2) Björn Hof (Delft University of Technology, at present University of Manchester), Jerry Westerweel (Delft University of Technology), Tobias Schneider en Bruno Eckhart (both Philipps-Universität Marburg)
The research has also been financially supported by The Foundation for Fundamental Research on Matter (FOM), the British Research Council and the Deutsche Forschungsgemeinschaft. Technical support was provided by the Dorset Tube Company.
For more information, please contact: Professor dr. Jerry Westerweel, Delft University of Technology, phone +31 (0)15 278 68 87.