SGenerations of aerodynamicists, meteorologists, fluid dynamics engineers and, more recently, wind power engineers have struggled with the enormous complexity of turbulent flows. As with many other phenomena, the underlying physical laws are well known. But their concrete application is difficult to tame mathematically and requires a simplified description.
In particular, it is about the question of how the energy in a flow is initially converted from large-scale turbulences through ever smaller turbulences into thermal energy through friction within the medium. We know the phenomenon from the coffee cup when, when stirring, a large vortex drags smaller and smaller vortices behind it like a train, which eventually slow down until the liquid becomes calm again.
In 1941, the Russian mathematician Andrei Kolmogorov formulated a universal power law for turbulent flows, which was used to calculate dissipation – i.e. the conversion of kinetic energy into heat energy – for the first time. According to Kolmogorow’s power law, only two factors are decisive: on the one hand, the energy introduced and, on the other hand, the viscosity of a substance – i.e. its greater or lesser viscosity. Kolmogorov’s universal formula is often only approximately fulfilled. In practice, numerous models are therefore used in which the exponents of the power law are modified on different scales.
Flow law put to the test
Recent experiments in the wind tunnel at the Max Planck Institute for Dynamics and Self-Organization (MPI-DS) in Göttingen now show that reality is much more complex than expected. The researchers led by Eberhard Bodenschatz, director at the MPI-DS, have succeeded in measuring the behavior of turbulent flows in detail – over large parameter ranges that were previously not accessible experimentally.
As the study published in “Physical Review Letters” explains, The measurements certainly seem to indicate certain universalities, but there were also systematic deviations from Kolmogorov’s predictions. “There is currently no theoretical model that would be consistent with the observed behavior,” says Bodenschatz. “The measurements are also a big surprise for us.”
The wind tunnel at the Max Planck Institute in Göttingen offers unique opportunities to research turbulent flows in detail. It is a high-pressure wind tunnel that uses the heavy gas sulfur hexafluoride (SF6) is working. This is compressed up to 15 bar. The turbulence behavior corresponds to that of normal air at around 120 bar. This high pressure makes it possible to achieve extreme degrees of turbulence in a compact space and to recreate the dynamics of larger air masses.
On the one hand, there is also particularly fine sensor technology with which the scientists can measure turbulent flows down to scales of around 20 micrometers. On the other hand, this wind tunnel has another special feature: an active grid made up of special flaps that can be controlled individually, so that different types of turbulent flows can be specifically recreated in the wind tunnel.
Snapshots of turbulent flow
The sulfur hexafluoride flows through the wind tunnel at a speed of up to five meters per second. The turbulence behavior is then determined a few meters behind the active grid, and the increasingly smaller vortices within the larger vortex structures – and thus the dissipation of the flow energy – are also precisely recorded in this way. “With this setup we can measure a huge range of parameters, far more than can be calculated with supercomputers today,” says Bodenschatz. The researchers took snapshots of the flow in the wind tunnel and determined the velocity field of the intertwined vortices.
The surprising behavior that the Göttingen scientists are now seeing when measuring different wave fields down to tiny scales at high levels of turbulence were able to demonstrate, has also made researchers elsewhere sit up and take notice. As the American turbulence researcher Andrew Bragg from Duke University in Durham writes in an accompanying commentary, The systematic deviations of real turbulence from the ideal case of the power law indicate that fundamental things are currently missing from today’s theories of turbulence. This also means that significant errors could still occur in the modeling of the Earth’s atmosphere. The currents in the Earth’s atmosphere are roughly well understood. But the tests in the wind tunnel indicate that unexpected gaps in detailed understanding could still arise in many areas.
The tests in the Göttingen wind tunnel initially serve basic research. But they are also very important for many applications. It’s not just technical trends that can still be optimized. Wake turbulence and turbulence also play an important role in wind power. When it comes to wind farms, the aim is to set up wind turbines as cleverly as possible so that they don’t slow each other down too much. The energy that drives them comes from the atmospheric flow in higher air layers and is converted near the ground by turbulent processes.
An improved understanding of turbulence is also crucial for meteorology. It is not yet possible to precisely calculate when it will start to rain in a moist, saturated cloud. Turbulent processes on different size scales play a crucial role here.
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