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.)
Under most circumstances, we think about flows changing from ordered and laminar to random and turbulent. But it’s actually possible for disordered flows to become laminar again. This is what we see happening in the clip above. Upstream, the flow in this pipe is turbulent (left). Then four rotors are used to perturb the flow (center). This disrupts the turbulence and causes the flow to become laminar again downstream (right). To understand how this works, we have to talk about one of the fundamental concepts in turbulence: the energy cascade.
Turbulent flows are known for their large range of length scales. Think about a volcanic plume, for example. Some of the turbulent motions in the plume may be a hundred meters across, but there are a continuous range of smaller scales as well, all the way down to a centimeter or less in size. In a turbulent flow, energy starts at the largest scales and flows further and further down until it reaches scales small enough that viscosity can extinguish them.
That should offer a hint as to what’s happening here. The rotors are perturbing the flow, yes, but they’re also breaking the larger turbulent scales down into smaller ones. The smaller the largest lengthscales of the flow are, the more quickly their energy will decay to the smallest lengthscales where viscosity can damp them out. This is what we see here. Once the turbulent energy is concentrated at the smallest scales, viscosity damps them out and the flow returns to laminar. Check out the full video below for a cool sequence where the camera moves alongside the pipe so you can watch the turbulence fading as it moves downstream. (Image and video credit: J. Kühnen et al.)
ETA: As it turns out, there’s more going on here than I’d originally thought. Simulations show that breaking up length scales is not the primary cause of relaminarization in this case. Instead, the rotors are modifying the velocity profile across the pipe in such a way that it tends to cause the turbulence to die out. The full paper is now out in Nature Physics and on arXiv.
Video footage of Iceland’s Grimsvotn volcano erupting shows a massive turbulentplume 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)
One of the characteristics of turbulence is its large range of lengthscales. Consider the ash plume from this Japanese volcano. Some of the eddy structures are tens, if not hundreds, of meters in size, yet there is also coherence down to the scale of centimeters. In turbulence, energy cascades from these very large scales to scales small enough that viscosity can dissipate it. This is one of the great challenges in directly calculating or even simply modeling turbulence because no lengthscale can be ignore without affecting the accuracy of the results. #
