The eddies and whorls seen in the flow of fluids have long been a source of fascination for scientists, the simultaneously coherent and unpredictable movements long eluding any unified theory to describe them. Collectively, this unpredictable motion is referred to as turbulence.
As there is still no theory derived from principle that can be used to describe turbulent flows, researchers in this domain instead rely on phenomenological models. The first of these was introduced in the 1940s by Soviet scientist Andrey Kolmogorov which, as of today, remains the reference theory for describing turbulent flows, in applications ranging from engineering to atmospheric modelling and medicine.
Over time, people have tried to challenge Kolmogorov’s theory to see if it holds true in the face of rigorous testing. One of the building blocks of the theory is that the energy distribution of turbulent flows all follow a similar pattern, known as the −5/3 power law. But while Kolmogorov originally derived this rule in a simple setup, real turbulent flows tend to be more complex, and it is in these more complex situations that the rule begins to falter.
To be able to challenge Kolmogorov’s predictions, one of two routes must be taken. Carrying out field experiments, for example taking real measurements of turbulence in the atmosphere or ocean, is one of these. The other involves using high-performance computers to do extremely large direct numerical simulations, and this is the path down which Professor Alessandra Sabina Lanotte’s career has taken her.
As a theoretical physicist specialising in numerical simulations of fluid dynamics problems, Lanotte has a particular interest in investigating turbulent flows. “The disorder and chaos of turbulence means that it is as yet impossible to know for certain the characteristics of a flow at any specific moment in time or point in space,” she says. “Instead, what we do is to try and work out the average properties of the flow, as well as what happens at the extremities of the energy distribution – the rare events. These rare events are important because they are often associated with failure in engineering, for example when wind turbines break in extreme conditions.”
In a recent PRACE project, Lanotte simulated turbulent flows to gain a better understanding of such flows seen in the ocean. The simulations looked at water in elongated geometries much larger on the horizontal axis than the vertical axis, much like the ocean. Effects such as rotation and stratification were then introduced, either matching the levels seen in the ocean or pushing them to their upper limits to gain a fuller understanding of the resulting turbulent phenomena.
“The difference between our work and what had been done previously by other researchers was that we did not use standard forcing,” says Lanotte. “All turbulent flows need energy injected into them to keep them alive, otherwise the energy in the flow eventually degrades into heat and the turbulence disappears. The problem is that it is usually impossible to distinguish the effects of the waves and the vortices in such forcing. What we did was to inject these types of energy separately to disentangle their roles in the turbulent flow.”
Amplitude of a turbulent velocity field confined in a thin layer
Lanotte’s team is still analysing their results, so they still do not know whether the Kolmogorov spectrum is always maintained, or if there are deviations away from it. “Working on this project has been a struggle at times due to the pandemic – I never once saw the students I was working with throughout the whole course of the project!”, says Lanotte. “But the results we have obtained so far have been collated into a PhD thesis by Vincenzo De Toma, and hopefully we will then be able to have some papers published.”
Looking forward, one of the team’s main goals is to refine the models of small-scale turbulence used in meteorology and oceanography to provide better overall predictive powers. “When running global circulation simulations to describe the ocean and the atmosphere, whether it be for short-term weather forecasting or for predicting long-term climate change, you can never fully simulate all of the motions at all scales. You have lower limits, and beyond them you must use models.
“All of the models used in such cases are based on Kolmogorov’s laws, so if we are able to correct these somehow, or provide some pointers as to when and where these laws might start to break down, then we can help improve the overall predictive powers of these types of simulation. We are working alongside an oceanographer from the United States who is helping us to integrate our work into such simulations.”
Lanotte believes that the power and importance of numerical simulations has yet to be fully appreciated in the minds of scientists and the wider public. “I work in an institute where most of the people are experimentalists,” she says. “When I talk to them about numerical simulations, I often get the impression that they think these take a couple of minutes on my desktop computer! It is important for the next generation of scientists to understand that carrying out numerical simulations on Tier-0 resources like those provided by PRACE is a huge undertaking, as challenging as the largest lab experiments. In the future, I think students need to be introduced to this kind of work at the undergraduate level.”