October 15, 2019 - by Simone Ulmer

For engineers from all disciplines, turbulence is an important topic in the construction of buildings, cars, planes, ships and submarines. But up until now, engineers have only been able to take turbulence into account using approximate models and idealized assumptions. Peter Vincent, Reader in Aeronautics at Imperial College London and his team are using complex computer simulations to investigate the chaotic motions of turbulence in more detail, leading to enhanced understanding and improved models.

The Millennium Prize Problem

The famous physicist Richard Feynman describes turbulence as one of the greatest unsolved problems in classical physics.  "In fact, a full understanding of the mathematics that underpins turbulence remains one of the unsolved Millennium Prize Problems today," says Vincent. Engineers therefore have often used approximate models to obtain their designs. However, the latest study from the researchers at Imperial College is now shedding new light on the dynamics and thus the mathematical-physical description of chaotic turbulence.

The team sought to learn more about channel flow, one of the most fundamental canonical flows. Properties of channel flow in the laminar regime, when the flow is smooth, have been understood for decades. However, things are far more complicated when the flow becomes turbulent. With "Piz Daint" from the Swiss National Supercomputing Centre (CSCS) and "Wilkes", a computer at Cambridge University, Vincent and his team simulated thousands of turbulent channel flows, each requiring billions of calculations. Specifically, each channel flow was subject to a small perturbation. By combining and processing the data from all simulations, the team was able to identify, for the first time, eigenmodes of the averaged decay of these perturbations. These are analogous to eigenmodes of the so-called Orr-Sommerfeld equation that governs behavior in the laminar regime.

New findings

The fact that the eigenmodes exist at all provides, according to the researcher, direct evidence that the system governing small amplitude perturbations to a turbulent channel flow is linear – like the analogous system for the laminar case. “Moreover, we found that one of the eigenmodes is complex and hence oscillatory, which implies that the governing equations cannot possess certain symmetries, which are often assumed by existing models,” Vincent points out.

The results provide new insights into the physics of turbulent flows and the researchers hope that their findings will enable the development of new, more accurate models for the averaged properties of turbulent flow. "These could be used by engineers around the world to develop the next generation of aircraft, wind turbines, submarines and more," Vincent says.

More about Peter Vincent’s research work: https://www.imperial.ac.uk/people/p.vincent


Iyer AS, Witherden FD, Chernyshenko IS & Vincent PE: Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow, Journal of Fluid Mechanics 2019, DOI: https://doi.org/10.1017/jfm.2019.520