Photographer Jason Wright captures dramatic views of Hawaiian landscapes. Moments like these remind us of the spectacular power of the ocean and atmosphere around us. Just look at all that incredible turbulence! See more of Wright’s work on his Instagram and website. (Image credit: J. Wright; via Colossal)
Subsonic turbulence – like the random and chaotic motions of air and water in our everyday lives – is something we have only a limited understanding of. Our knowledge of supersonic turbulence, where shock waves and compressibility rule, is even more tenuous. In part this is because, although we can observe snapshots of supersonic turbulence in astronomical settings like the Orion Nebula shown above, we cannot watch it evolve. On these scales, features simply don’t change appreciably on human timescales.
This has limited scientists to mostly numerical and theoretical studies of supersonic turbulence, but that is starting to change. Researchers are now building experimental set-ups that collide laser-driven plasma jets to generate boundary-free turbulence at Mach 6. Thus far, the observations are consistent with what’s been seen in nature: at low speeds, the turbulence is consistent with Kolmogorov’s theories, with energy cascading from large scales to smaller ones predictably. But as the Mach number increases, the nature of the turbulence shifts, moving toward the large density fluctuations seen in nebulae and other astrophysical realms. (Image credit: F. Battistella; research credit: T. White et al.; see also Nature Astronomy; submitted by Kam-Yung Soh)
With some help from Physics Girl and her friends, Grant Sanderson at 3Blue1Brown has a nice video introduction to turbulence, complete with neat homemade laser-sheet illuminations of turbulent flows. Grant explains some of the basics of what turbulence is (and isn’t) and gives viewers a look at the equations that govern flow – as befits a mathematics channel!
There’s also an introduction to Kolmogorov’s theorem, which, to date, has been one of the most successful theoretical approaches to understanding turbulence. It describes how energy is passed from large eddies in the flow to smaller ones, and it’s been tested extensively in the nearly 80 years since its first appearance. Just how well the theory holds, and what situations it breaks down in, are still topics of active research and debate. (Video and image credit: G. Sanderson/3Blue1Brown; submitted by Maria-Isabel C.)
Turbulence – that pestersome, unpredictable, and chaotic state of flow – has been a thorn in the sides of mathematicians, physicists, and engineers for centuries. It is certainly one of – if not the – oldest unsolved problem in physics. Over at Ars Technica, Lee Phillips has a nice overview of the situation, including what makes the problem so difficult:
The Navier-Stokes equation is difficult to solve because it is nonlinear. This word is thrown around quite a bit, but here it means something specific. You can build up a complicated solution to a linear equation by adding up many simple solutions. An example you may be aware of is sound: the equation for sound waves is linear, so you can build up a complex sound by adding together many simple sounds of different frequencies (“harmonics”). Elementary quantum mechanics is also linear; the Schrödinger equation allows you to add together solutions to find a new solution.
But fluid dynamics doesn’t work this way: the nonlinearity of the Navier-Stokes equation means that you can’t build solutions by adding together simpler solutions. This is part of the reason that Heisenberg’s mathematical genius, which served him so well in helping to invent quantum mechanics, was put to such a severe test when it came to turbulence.
Phillips goes on to describe some of the many methods researchers use to unravel the mysteries of turbulence computationally, experimentally, and theoretically. This is a great introduction for those curious to get a sense of how turbulence, stability theory, and computational fluid dynamics all fit together. (Image credits: L. Da Vinci; NASA; see also: Ars Technica; submitted by Kam Yung-Soh)
Turbulence, the chaotic regime of fluid dynamics, is a complicated beast. It’s hard to analyze or predict, but we do understand some general ideas about it, like the fact that energy starts out in large eddies, cascades down smaller and smaller ones, and finally gets dissipated at the smallest scales, where viscosity snuffs them out. But that’s only true in three dimensions.
Two-dimensional turbulence – what you get when you confine your fluid to a flat plane – is even weirder. When turbulence is flat, you can actually get an inverse energy cascade, where the energy of small eddies can add up to feed bigger ones. For awhile, this was treated as a mathematical curiosity; after all, we live in a three-dimensional world. But there are situations in life that are nearly two-dimensional, like the surface of a soap bubble or the atmosphere of a planet (which is typically exceptionally thin compared to the planet’s radius). And, little by little, scientists are collecting evidence that this inverse cascade – a flow of energy from small scales to larger ones – does actually happen in the real world. Understanding how this works may explain why hurricanes can intensify even when conditions are “wrong” and how Jupiter’s Great Red Spot has persisted for centuries. To learn more, check out Quanta Magazine’s full article on the work. (Image credit: NASA et al., M. Appel; via Quanta; submitted by Kam-Yung Soh)
Turbulence, the seemingly random and chaotic state that fluids often tend toward, can be difficult to wrap one’s head around. Turn your faucet on high or pour milk into your coffee, and the flow just looks like a completely unpredictable mess. But there are important patterns to be found.These flows have many different lengthscales and timescales to them. Think of a cloud. There are very large-scale motions that are close to the size of the entire cloud, but there are also very small ones that may be only a centimeter or so in size.
Our best understanding of turbulence so far says that energy starts out in these large scales and slowly works its way down to the smaller ones, where viscosity (essentially friction, in this case) can transform that motion into heat. Above you see a creative way to display this fact. Using data from a numerical simulation, the authors transformed velocity information into these mandala-like patterns. The center of the image represents the large lengthscales, where energy is added. Moving around the circle, like a clock’s hand does, shows different positions in space. Moving radially from the center outward takes you through different lengthscales from large to small.
Notice how the large lengthscales break into smaller and smaller ones as you move outward. The pattern looks like a set of fractal pitchforks, with each lengthscale fracturing into smaller and smaller ones as the turbulence breaks down further. There’s lots more to see in the original poster, below, but you should really click here for the glorious full-size original. The poem, by the way, is the work of physicist Lewis Richardson, who wrote it to summarize how turbulence works. (Image credit: M. Bassenne et al.)
Space, as I’ve discussed previously, is surprisingly full of matter, especially clouds of dust. And yet the rate of star formation we observe is bizarrely low; the Milky Way, for example, produces only about one solar mass worth of new stars every year. If gravity were the sole force driving star formation, we’d see far more stars forming. Recent research suggests that turbulence plays a major role in regulating the star formation process, both by countering gravity’s attempts to collapse gases into a proto-star and by creating supersonic shocks that drive material together to jump-start star formation. There seem to be other important ingredients as well: young stars tend to form jets that blow material back into the interstellar clouds they’re forming in, feeding the turbulent background. For more, check out Physics Today. (Image credit: ESA/NASA/Hubble/ESO, via APOD; research credit: C. Federrath)
