Mathematician makes breakthrough in understanding of turbulence

November 15, 2012

(—A mathematician at the University of Glasgow is helping to find an answer to one of the last unsolved problems in classical mechanics.

Dr Andrew Baggaley, of the University's School of Mathematics and Statistics, has published a paper in the journal , which extends our understanding of the of fluids, commonly known as turbulence. The incredibly complex ways in which liquids and gases move and interact has proven very difficult for scientists to understand and predict.

A better understanding of turbulence in fluids would be tremendously helpful to a wide range of fields including weather forecasting, and astronomy.

Dr Baggaley has developed a mathematical model of how behaves on the when cooled to just a few degrees above (-273°C). At such extremely low temperature, liquid helium contains a both a normal fluid with an element of viscosity or friction but also what is known as a 'superfluid' – a rare state of liquid matter which is entirely frictionless.

Detailed of this help to understand the link between the apparently very different behaviours of superfluids on the quantum scale and more familiar classical, viscous, fluids all around us.

Dr Baggaley said: "We all have some basic understanding of turbulence from experiences in our everyday lives. For example, when we swim, the friction between our arms and the water excites complex motion at a lengthscale of a meter or so.

"When we get out of the pool, the motion of the water will eventually become still as the energy from the we created cascades into a series of smaller and smaller eddies. Ultimately, the kinetic energy from the motions of our arms is released through the rotation of the water at very small scales, and converted to heat.

"Nearly every fluid in the universe is affected by turbulence, just like the water in the pool. Although our understanding of the nature of turbulence is improving, the random, chaotic motion of those liquids and gases can't currently be entirely predicted."

At the quantum scale the behaviour of superfluids becomes a great deal more unfamiliar. Instead of creating random eddies of varying strength, rotational motion in frictionless superfluid helium spontaneously creates atomic-size holes of uniform size, around which the fluid circulates at uniform rate. In superfluid helium the holes, known as quantised vortices, are around 10 nanometres in width or about 10,000 times narrower than a human hair.

Dr Baggaley added: "We commonly think of turbulence as a collection of interacting eddies at different sizes. At very low temperatures, the weirdness of quantum mechanics becomes apparent and initially the fluid motion seems very different. The fluid loses its friction, rotational motion in the fluid is very limited, and these quantum vortices, which are like mini tornadoes, thread through the fluid.

"However, this work shows these small tornadoes have a tendency to bundle together and cause the quantum turbulence to have the same statistical properties as turbulence in a viscous fluid such as water. What initially seemed so strange becomes much more familiar.

"These similarities, combined with the simpler nature of these quantum fluids, provides the opportunity to cast an old problem in a new light and hopefully advance our understanding of fluid dynamics and turbulence.

"I'd hope that further research over the next 10 years or so will greatly deepen our understanding of both quantum and classical turbulence which could revolutionise the world we live in."

Dr Baggaley's paper, titled 'Vortex-Density Fluctuations, Energy Spectra, and Vortical Regions in Turbulence', is published in Physical Review Letters and is available from .

Explore further: Quantum memory and turbulence in ultra-cold atoms

Related Stories

Quantum memory and turbulence in ultra-cold atoms

July 20, 2009

Scientists at MIT have figured out a key step toward the design of quantum information networks. The results are reported in the July 20th issue of Physical Review Letters and highlighted in APS's on-line journal Physics.

Turbulent flows in 2D can be calculated in new model

October 23, 2012

Turbulent flows have challenged researchers for centuries. It is impossible to predict chaotic weather more than a week in advance. Wind resistance on a plane or a car cannot be calculated precisely, since it is determined ...

UW Mathematician to Study Tornado Turbulence

July 26, 2006

Anyone who has seen a tornado has noticed its snake-like core weaving from an imaginary hole in the sky to threaten the ground below. However, not everyone who has witnessed a tornado calls it a "vortex filament" and views ...

Energy simulation may explain turbulence mystery

February 26, 2009

( -- A new 3D model linking magnetic fields to the transfer of energy in space might help solve a physics mystery first observed in the solar wind 15 years ago.

Recommended for you

New type of electron lens for next-generation colliders

October 18, 2017

Sending bunches of protons speeding around a circular particle collider to meet at one specific point is no easy feat. Many different collider components work keep proton beams on course—and to keep them from becoming unruly.

1 comment

Adjust slider to filter visible comments by rank

Display comments: newest first

1 / 5 (1) Nov 18, 2012
Those vortices are pathways for magnetic fields, so to understand the banding of those vortices and in effect the turbulence one might look into the behavior of magnetic fields on the quantum scale.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.