Most people are only consciously aware of the existence of turbulence when the pilot announces it. But apart from the discomfort of a bumpy flight, turbulence affects us in many other important aspects of daily life. The fact that turbulent mixing is much more efficient than molecular diffusion does not only come in handy when stirring the tea after adding sugar and milk (whether it is better to first put the milk or the tea into the cup can be discussed in another blog entry), but also has impacts on important problems in medicine, engineering, biology and physics, to name just a few. Turbulence is responsible for noise created at the blades of wind turbines and knowledge about it can help engineers to design quieter wings. It also affects the delivery of drugs to the lung, and therapeutic aerosols can be designed to optimise their effect in the body by modifying their aerodynamic properties. Turbulent effects are important for designing efficient filters for power plants or improving the efficiency of fuel engines. For our weather, turbulence plays a critical role. For example, it controls the exchange of heat and moisture between the soil and the atmosphere and is one of the factors which influences the development and characteristics of clouds. This is the reason why it is of so much importance for weather forecast models to describe turbulent processes accurately.
Unfortunately, the importance of turbulence is directly proportional to the difficulty to study its properties. The underlying set of equations which describe all fluid flows are the Navier-Stokes equations. This set of equations is extremely difficult (and most of the times impossible) to solve analytically. This is why for most real-world applications computer models are used which are able to find numerical solutions of the Navier-Stokes equations with good precision. Especially for turbulent flows, these computer models are numerically very expensive and the direct numerical simulation of turbulent flows remains restricted to relatively simple cases. In most applications, a certain level of approximation for the smaller scales, or even the whole turbulent part of the flow, is necessary to be able to simulate turbulent flows. This is necessary despite the fact that computer performance has rapidly increased over the last decades.
When the first numerical weather forecast was computed by hand by Lewis F. Richardson in 1922, it took him 6 weeks to calculate a 6-hour forecast for Europe. This forecast, apart from coming approximately 5.96 weeks too late, was also wrong. Nevertheless, his work was revolutionary and kicked off the era of numerical weather forecasts. In the publication of his results he estimated that it would take 64000 human computers (people who solve the numerical equations by hand) to simulate the global weather in real-time (meaning it would take one hour to compute a one hour forecast). He envisioned a weather centre in which hundreds of human computers would work together solving the equations for their respective parts of the forecast domain, and coordinators would make sure that everybody stays in sync, collect the results for each time step from the human computers and unify them to one big data set. He basically described the parallelisation of numerical flow models, including the communication between the “nodes”, which decades later would be used to compute global weather forecasts in only a few hours on modern supercomputers.
One of the first supercomputers was the CDC 6600. In 1964 it was considered to be the most powerful computer in the world and could compute an astonishing three million floating point operations per second (3 megaflops). Today’s fastest supercomputer is the IBM Summit which is able to perform 122×1015 floating point operations per second, 40 billion times more than the CDC 6600. Despite this impressive increase in computational power, current supercomputers are still not fast enough to allow the direct simulation of turbulent flows for most real-life applications, leaving plenty of interesting research topics for current and future scientists to investigate.
Richardson, L. F., 1922: Weather prediction by numerical process. Cambridge university press, 236 pp.