March 06, 2006
Fluid Turbulence is everywhere in the world around us. It impacts all of us on a daily basis, be it in stirring milk into our morning cup of coffee, mixing combustion gases in a burner, or in the spread of pollutants or bioagents in the atmosphere. Biologists are trying to learn how animals seek out partners and prey following scents transported by turbulent wind and water flows. Turbulence also influences how likely it is that two agents will come together and react chemically - how pollution or poisons spread out and fluctuate across oceans and air. Turbulence also affects how clouds form and atmospheric ozone gets depleted.
Turbulence occurs naturally when a fluid, like air or water, is pushed at high speeds or at a large scale, and is characterized by chaotic, seemingly random flow patterns. It is most easily recognisable when "particles" are tossed around in a flow, like when leaves dance in an autumn wind or ribbons of mist appear behind a car speeding over a wet highway. For decades scientists have been trying to understand how exactly turbulence happens. One of their key questions has been: when particles start out near each other, how long does it take for turbulence to separate them? In the 1920s, a British scientist, Lewis Fry Richardson, predicted that the mean-square separation of a fluid element pair should grow as the third power of time. This result, known as the Richardson-Obukhov law, is commonly used in models of transport in turbulence. Because of turbulence’s high complexity, the law assumes that flow separation is independent of the original distance between the particles.
In the 1950s, however, the Australian George Batchelor in Cambridge devised another separation formula which was indeed dependent on the initial distance between particles. He saw the pair separation as increasing with time squared, and further suggested that the Richardson-Obukhov law would, in the long-run, be obeyed.
Now a German-French-United States research team, led by Professor Eberhard Bodenschatz, has experimentally tested both theories. They created a particle tracking system out of three high-speed cameras and a very bright laser (images 2, 3). The scientists put very small particles into turbulent water flows (image 1) and measured the particle movements. The cameras recorded the distance between particles over 25,000 times per second. This is about a million times smaller and faster than the movement of two snowflakes in a snowstorm.
The researchers found results in excellent agreement with Batchelor's predictions, but which did not observe the Richardson-Obukhov law. Contrary to common expectations, Batchelor’s formula appears to predict particle movement in just about all turbulent flows on Earth; particle separation distance may indeed have its influence. The measurements also suggest that particles move more slowly away from each other than previously assumed.
These results could have implications for a number of fields of science and engineering, from efficiently mixing industrial materials to modelling the interiors of stars.
This project was supported by the US National Science Foundation, Cornell University, and the Max Planck Society.