Turbulent flows are ubiquitous, but they’re also mindbogglingly complex: ever-changing in both time and space across length scales both large and small. To try to unravel this complexity, scientists use simplified model problems. One such simplification is Kolmogorov flow: an imaginary flow where the fluid is forced back and forth sinusoidally. This large-scale forcing puts energy into the flow that cascades down to smaller length scales through the turbulent energy cascade. Here, researchers depict a numerical simulation of a turbulent Kolmogorov flow. The colors represent the flow’s vorticity field. Notice how your eye can pick out both tiny eddies and larger clusters in the flow; those patterns reflect the multi-scale nature of turbulence. (Image credit: C. Amores and M. Graham)
Tag: Kolmogorov
Testing Turbulence’s Limits
Understanding chaotic, turbulent flows has long challenged scientists and engineers due to their sheer complexity. In turbulent flows, energy cascades from the largest scales — like the kilometer-size cross-section of a cloud — to the very smallest scales, less than a millimeter in size, where viscosity transforms the flow’s motion to heat. For nearly a century, our theoretical understanding of turbulence has posited that there are certain universal behaviors in the statistics of a turbulent flow — essentially that, due to this energy cascade, some aspects of every turbulent flow are the same from clouds to ocean currents to your coffee cup.
Accordingly, experimentalists have tried for decades to measure this expected universality. Often, there are some signs of agreement, and any deviation was attributed to the finite difference between the large and small scales of the flow. (The theory assumes the difference in these scales’ size is effectively infinite.) But now researchers have achieved the largest range of scales yet — comparable to those found in the atmosphere — and the gaps between theory and experiment remain. The new study does show signs of universality but in a different way than existing theory predicts. As the authors point out, we’ll need new theories to explain these findings. (Image credit: D. Páscoa; research credit: C. Küchler et al.; via APS Physics)
An Introduction to Turbulence
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.)
Turbulent Flames
The flames surrounding a burning tree stump flicker and billow in this image from photographer Serdar Ozturk. The chaotic motion of the flames is indicative of turbulence, a state of fluid flow known for its many scales. Note the range of lengthscales and structures in the fire. In turbulent flows, kinetic energy cascades from large scales, like the width of the top of the plume, down to the small scales, which may be even smaller than the wisps of flame at the edges of the fire. At the largest scales, the structures and behaviors we observe are all flow- and geometry-dependent, but theory predicts that, at the smallest scales, all turbulent flows look the same. (Photo credit: trashhand/Serdar Ozturk)
Volcanic Ash Plume
Video footage of Iceland’s Grimsvotn volcano erupting shows a massive turbulent plume of ash. The largest scales of the plume are of the order of hundreds, if not thousands of meters, and the eddies of the plume appear to move very slowly, especially far from the base. According to Kolmogorov, however, at the smallest scales of the flow (< 1 mm), the turbulent motions are isotropic. No one has been able to achieve Reynolds numbers high enough to fully prove or disprove Kolmogorov’s hypothesis, but natural events like volcanic eruptions produce some of the largest Reynolds numbers on earth. (See also: interview with videographer; via Gizmodo, jshoer)
