Steve Mould is back with another video looking at wild fluid behaviors. This time he’s considering hose instabilities like the one that makes a water-carrying hose beyond a certain length to whip wildly back and forth. He tries to track down the reasoning for these flexible hoses snapping and whipping. In truth, both the hoses and the wind dancers do their thing due to interactions between the elasticity of the hose and the fluid dynamics of the flows within. These applications are ripe for a few control volume thought experiments. (Video and image credit: S. Mould)
The butterfly effect — that the flapping of a butterfly’s wings in Brazil can cause a tornado in Texas — expresses the sensitivity of a chaotic system to initial conditions. In essence, because we can’t possibly track every butterfly in Brazil, we’ll never perfectly predict tornadoes in Texas, even if the equations behind our weather forecast are deterministic.
But this interpretation doesn’t fully capture the subtleties of the situation. With fluid dynamics, the small scales of a flow — like the turbulence in an individual cloud — are linked to the largest scales in the flow — for example, a hurricane. For short times, we’re actually quite good at predicting those large scales; our weather forecasts can distinguish sunny days and cloudy ones a week out. But at smaller scales, the forecast errors pile up quickly. No one can forecast that an individual cloud will form over your house three days from now. And because the small scales are linked to the larger scales, the uncertainties from the small scale cascade upward, limiting how far into the future we can reliably predict the weather.
And, unfortunately, drilling down to capture smaller and smaller scales in our models can’t fix the problem, unless our initial uncertainties are identically zero. To get around this problem, weather forecasters instead use ensemble forecasting, where they run many simulations of the weather with slightly different initial conditions. Those differences in initial conditions let the forecasters play with those initial uncertainties — how accurate is the temperature reading from that station? How reliable is the instrument reporting that humidity? How old is the satellite data coming in? Once all the forecasts are run, they can see how many predicted sunny days versus rainy ones, which ones resulted in severe weather, and so on. Often the probabilities we see in our weather app — like 30% chance of rain — depend on factors including how many of the forecasts resulted in rain.
Unfortunately, this butterfly effect permanently limits just how far into the future we can predict weather — at least until we fully understand the nature of the Navier-Stokes equations. For much more on this interesting aspect of chaos, check out this Physics Today article. (Image credit: NASA; see also T. Palmer at Physics Today)
Fluid dynamics is a veritable playground of chaotic systems, but that doesn’t always translate to easy explanations, as Henry Reich points out in this Minute Physics video. The common metaphor for chaos is the Butterfly Effect, an idea that a butterfly flapping its wings causes a typhoon on the other side of the world. I agree with Henry that this is a poor example of chaos, for many of the same reasons he lays out. In reality, we call a system chaotic when its outcome is so sensitive to the initial conditions that the result becomes effectively unpredictable. And there are some very simple systems that are chaotic, like a double pendulum or a three-body problem. The weather is, honestly, too complicated of a system for the metaphor to make sense, but fluid dynamics does have other, simpler examples, like mixing in porous media, bouncing droplets, or, my personal favorite, the fluid dynamical sewing machine. (Video credit: Minute Physics)
One of the peculiar characteristics of viscous, laminar flows is that they are reversible. Squirt dye into glycerin, stir it one way, then the opposite direction, and the dye returns to its initial position. But this neat trick only works in simple geometries; in a more complex environment, like the pores between packed gravel, flows cannot make their way back to their initial state.
That’s the idea at the heart of this new study of mixing in porous media. Researchers took a bed of packed beads and pushed a slow, steady flow of dye into the bed. Then they steadily withdrew fluid to reverse the flow and observed how the dye they’d injected appeared at the surface of the bed (top image). If the flow were perfectly reversible, we’d expect the dye to return to its injection point. But instead the dye is spread chaotically across the surface, giving researchers a snapshot of the chaotic mixing taking place between beads. (Image and research credit: J. Heyman et al.; via APS Physics)
When we think of resonance, we often think of it in simple terms: hit the one right note, and the wine glass will shatter. But resonance isn’t always about a one-to-one ratio between a driving frequency and the resonating system. Especially in fluid dynamics, we often see responses that occur at other, related frequencies.
One of the simplest places to see this is with a droplet bouncing on a bath of fluid. Above you see a liquid metal droplet bouncing on a bath of the same metal. At low amplitude, the pool surface moves at the driving frequency and a droplet bounces simply upon that surface, with one bounce per oscillation. Increase the amplitude, though, and the droplet’s bounce changes. It bounces twice – one large bounce and one small bounce – in the time it takes for the pool surface to go through one cycle. This is called period doubling because the bouncing occurs at twice the driving frequency.
Turn the amplitude up further, and the system undergoes another change. Faraday waves form on the surface. They resonate at half the driving frequency, and a droplet’s bouncing will sync up with the waves. That means the droplet returns to a one-to-one bounce with the waves, but the waves themselves are no longer reacting at the driving frequency. It’s this kind of complexity that makes fluid systems fertile grounds for studying paths toward chaos. (Image and research credit: X. Zhao et al.)
One of the great challenges in fluid dynamics is understanding how order gives way to chaos. Initially smooth and laminar flows often become disordered and turbulent. This video explores that transition in a new way using sound. Here’s what’s going on.
The first segment of the video shows a flat surface covered in small particles that can be moved by the flow. Initially, that flow is moving in right to left, then it reverses directions. The main flow continues switching back and forth in direction. This reversal tends to provoke unstable behaviors, like the Tollmien-Schlichting waves called out at 0:53. Typically, these perturbations in the flow start out extremely small and are difficult or even impossible to see by eye. So researchers take photos of the particles you see here and analyze them digitally. In particular, they are looking for subtle patterns in the flow, like a tendency for particles to clump together with a consistent spacing, or wavelength, between them. Normally, researchers would study these patterns using graphs known as spectra, but that’s where this video does something different.
Instead of representing these subtle patterns graphically, the researchers transformed those spectra into sound. They mapped the visual data to four octaves of C-major, which means that you can now hear the turbulence. When the audio track shifts from a pure note to an unsteady warble, you’re hearing the subtle disturbances in the flow, even when they’re too small for your eye to pick out.
The last part of the video takes this technique and applies it to another flow. We again see a flat plate, but now it has a roughness element, like a tiny hockey puck, stuck to it. As the flow starts, we see and hear vortices form behind the roughness. Then a horseshoe-shaped vortex forms upstream of it. Aside from the area right around the roughness, this flow is still laminar. But then turbulence spreads from upstream, its fingers stretching left until it envelops the roughness element and its wake, making the music waver. (Video and image credit: P. Branson et al.)
A wall of lava lamps in a San Francisco office currently helps keep about 10% of the Internet’s traffic secure. Internet security company Cloudflare uses a video feed of the lava lamps as one of the inputs to the algorithms they use to generate large random numbers for encryption. The concept dates back to a 1996 patent for a product called LavaRand. The idea is that using a chaotic, unpredictable source as a seed for random number generators makes it much harder for an adversary to crack your encryption.
With lava lamps, a lot of that chaos comes from the fluid dynamics involved – without perfect knowledge of thousands of variables, it would be impossible to simulate the lava lamp wall and get the same outcome as the real one – but there’s also randomness that comes from the measurement. People walking by, shifts in lighting, and random fluctuations of individual pixels all help make the video feed unpredictable. For those interested in the details of how Cloudflare uses their lava lamps, the company explains things for both technical and non-technical readers. You can also check out Tom Scott’s video for a good overview. (Image and video credit: T. Scott; submitted by Jean H.)
In industry, tanks are often agitated or stirred to mix different elements. The goal is to create a laminar but chaotic flow field throughout the mixture. Introducing particles to such a system reveals that things are not quite as chaotic as they might seem. The photographs above show the pathlines of various large, glowing particles initially poured into the tank from above. Over time, the particles scatter off of structures in the mixed sections of the tank and end up trapped in vortex tubes that form above and below the agitator. Once trapped in the vortex tube, the particles follow helical paths inside the tube, creating patterns like those seen in the lower two photos. (Image and research credit: S. Wang et al., 1, 2, 3)
As kids, most of us got in trouble at some point for blowing through a straw into our nearly-empty drinks. What you see here is a consequence of such misbehavior, though in this case the fluid is silicone oil and the straw is a metal needle (not shown) through which helium is continuously injected beneath the liquid surface. Depending on the angle of the straw, different behaviors are observed, as seen in this video. The photo above shows an intermediate regime, in which tiny jets form at the surface and eject a stream of drops. Each drop sails in a little parabolic arc and briefly bounces on the surface, like the drops on the right, before coalescing into the pool. (Image credit: J. Bird and H. Stone; video)
A group at MIT have created a new 3D printer that builds with molten glass. This allows them to manufacture items that would difficult, if not impossible, to create with traditional glassblowing or other modern techniques. One of the coolest aspects of this technique is that it can use viscous fluid instabilities like the fluid dynamical sewing machine to create different effects with the glass. You can see this around 1:56 in the video. Varying the height of the head and the speed at which it moves will cause the molten glass to fall and form into different but consistent coiling patterns. All in all, it’s a very cool application for using some nonlinear dynamics! (Video credit: MIT; via James H. and Gizmodo)
