Scientists build a bridge over turbulent waters

This is what causes clouds to break open suddenly with rainstorms. A lack of this weakens the bones of astronauts within months in space. Weaker water-borne creatures survive in their ecosystem due to this. A physicist could go on roll-calling the instances of this ubiquitous and important phenomenon they call turbulence: the restless, swirling and semi-random behaviour of fluids. It is also the last great fort of classical physics scientists are yet to storm. But, a paper published recently in the Physical Review Letters by scientists from the University of Illinois, Urbana-Champaign, has just heated up the offensive.

 

The paper has explained a pivotal experiment on turbulence conducted 73 years ago by Johann Nikuradse.

 

He had found that when fluids pass through a rough pipe an odd thing happens, the friction experienced by the fluid decreases as the speed of the fluid rises till suddenly after a point the friction begins to increase before settling to a constant value. Without a theoretical framework for this phenomenon, engineers and scientists have had to refer to elaborate charts and graphs based on Nikuradse’s data when working on topics ranging from aerodynamics to construction of oil pipes.

 

“Our explanation of Nikuradse’s results is based on a conceptual model of turbulence that goes back to Leonardo Da Vinci, who pictured turbulence as made up of many locally swirling motions, all jumbled up.

 

The results will make it possible for engineers to calculate the friction from first principles, instead of having to rely on a chart or table,” explains Gustavo Gioia, who authored the paper with his student Pinaki Chakraborty.

 

Nikuradse’s experiment and consequently its theoretical explanation by Gioia et al are of fundamental importance to turbulent flow. Gioia says, “In pipelines that transport oil and gas, the cost of pumping is proportional to the friction. Understanding and controlling the friction could save millions of dollars a year.

 

“It is not a matter of pipes only, but also open channels, such as rivers and flood plains. Our work is relevant to hydraulics engineering, hydrology, geomorphology, etc. In fact, our work is relevant to turbulent flows over all sorts of rough surfaces — the surface of a submarine, the wings of an airplane and the scaled skin of a fish.”

 

The paper by their colleague Nigel Goldenfeld is closely related to their work. Goldenfeld’s work provides a long-sought-after link between turbulence and phase transitions.

 

 

 

As you turn on the tap, the initial stream of water is clear and smooth. But, as you keep turning the knob, you reach a point when this steady stream suddenly degenerates into an unclear pillar of spluttering water. The water is the same, but now there are eddies and vortices on the surface of the stream, which render the flow unclear. This is called turbulence.

 

 

Any flow is governed by the Navier-Stokes equations. In principle, one could answer any question about turbulence and make predictions by solving these equations. But, they are so difficult that no current supercomputer can effectively compute solutions from these equations.

 

 

Provides a mathematical approximation which can be used to make predictions about turbulent flow, and to make theoretical sense and give an interpretation to complicated experimental results.