Here on Earth, placing a denser fluid over a lighter one creates an unstable equilibrium. Thanks to gravity, the heavier, denser fluid wants to sink and the lighter fluid wants to rise. Any small disturbance will kick this into action, just like a tiny nudge can send a ball rolling down the hill. For the fluid, that nudge manifests as waviness in the interface between the two fluids. That waviness will quickly grow into billows like those shown above as the Rayleigh-Taylor instability takes over and the heavy (clear) fluid trades places with the lighter (green) fluid. You’ve probably witnessed this effect yourself when pouring milk into iced coffee. To see it in action, check out the video of this experiment or my FYFD video on the Rayleigh-Taylor instability. (Image credit: M. Davies Wykes)
Search results for: “waves”
Shock Waves in Flight
This week NASA released two new images of the shock waves surrounding T-38C jets in free flight. They’re the result of NASA’s new adaptations of the schlieren photography technique, which has let scientists visualize shock waves (in the lab, at least) for more than a century. To celebrate, I thought it would be fun to demonstrate some of the data engineers can extract from images like the one above. So I’m going to show you how to calculate how fast this plane was flying!
Shock waves depend a lot on geometry. This is not too surprising, really, since shock waves are nature’s way of quickly turning the air because there’s an object in the way. This leads to a very powerful observation, though: the angle of a shock wave depends on the geometry of the object and the Mach number of the flow. (The Mach number is the ratio of an object’s speed to the local speed of sound, so an object moving at Mach 1 is moving at the speed of sound.)
The reverse observation is also true: if we can measure the angle of a shock wave from a known geometry, then we can calculate the Mach number. Now, I don’t have any special information about the geometry of a T-38, so most of the shock waves in this picture can’t tell me much quantitatively.
But, it turns out, I don’t need to know anything about the geometry of the plane to figure out its Mach number. That’s because that very first shock wave over on the right is coming off a sharp probe mounted over the airplane’s nose. The probe is sharp enough, in fact, that I can treat it as though it’s a tiny point disturbance. That means that rightmost shock wave is a special kind of shock known as a Mach wave, and its geometry depends solely on the Mach number. It’s a pretty simple equation, too:
So, all I have to do is fire up some software like GIMP or ImageJ and estimate the angle of that first shock wave.
I came up with an estimate of about 77 degrees for the shock wave angle, which gives Mach 1.026 for the plane’s speed. Keep in mind that a) I’m using a grainy photo; and b) I have no information about the plane’s orientation relative to the camera. Nevertheless, NASA’s caption reports that this plane was moving at Mach 1.05 in the picture. My quick and dirty estimate is only off by 2%!
Of course, engineers are interested in a lot more than estimating an aircraft’s speed from these photos. With a little more geometry information, they can gather a lot of useful data from these images. One of the goals for the new photography technique is to help study new aircraft designs that generate weaker shock waves and quieter sonic booms. (Original images: NASA)
Seeing Blast Waves
With a large enough explosion, it’s actually possible to see shock waves. This high-speed camera footage shows the detonation of a car packed with explosives. After the initial flash, you can see the thin membrane of the blast wave expanding outward. This shock wave is a traveling discontinuity in the air’s properties–temperature, pressure, and density all change suddenly over an incredibly small distance. It’s this last variable–density–that enables us to see the effect. Density has a significant impact on air’s index of refraction (which also explains heat mirages). In this case, the shift in refractive index is large enough that we see the difference relative to the background, enabling our eyes to follow an otherwise invisible effect. (Video credit: Mythbusters/Discovery Channel; via Gizmodo)
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Waves Over the Rockies
These spectacular wave-like clouds are the result of the Kelvin-Helmholtz instability. When two layers of air move past one another at different velocities, an unstable shear layer forms at their interface. Disturbances in this shear layer grow exponentially, creating these short-lived overturning waves that quickly turn turbulent. The strong resemblance of these clouds to breaking ocean waves is no coincidence–the Kelvin-Helmholtz instability occurring between the wind and water is what generates many ocean waves. Kelvin-Helmholtz patterns are also common on other planets, like Jupiter, Saturn, and Mars. (Image credit: Breckenridge Resort; submitted by jshoer)
Shock Waves in Flight
Schlieren optical systems have been used to visualize shock waves in labs for more than a century, but the technique did not translate well to photographing shock structures outside the lab. But now NASA’s Armstrong Research Center and Ames Research Center have developed a method that allows them to capture highly-detailed images of the shock waves around airplanes while they are flying. This is incredible stuff. Be sure to check out the high-resolution versions on this page, along with more description of the coordination necessary to pull off the photos.
The light and dark lines you see emanating from the airplane are places with strong density gradients. The dark lines are mostly shock waves, with the strongest shock waves appearing black due to the large change in air density. Many of the light streaks are expansion fans, areas where the density and pressure drop as air speeds up.
The goal of this research is to better understand shock wave structures around supersonic planes in order to reduce the noise supersonic aircraft cause when flying overhead. As you can see in the photos, the shock waves at the nose and tail of the aircraft persist far away from the aircraft; these are what cause the twin sonic boom heard when the plane flies by. (Photo credit: NASA; via J. Hertzberg)
Blast Waves Visualized
Typically, shock waves are invisible to the human eye. Using sensitive optical techniques like schlieren photography, researchers in a lab can visualize sharp density gradients like shock waves or even the slight density variations caused by natural convection. But it takes some special conditions to make shock waves visible to the naked eye. The blast wave of the explosion in the photo above is a great example. The leading edge of the shock wave and the heat of the explosion create a strong, sharp change in density. That density change is accompanied by a change in the air’s refractive index. As light travels from the distance toward the camera, it’s distorted–more specifically, refracted–when it travels through the blast wave and its wake. And, in this case, that visual distortion is strong enough that we can clearly see the outlines of the shock waves moving out from the explosion. The apparent horizontal line through the blast wave is probably the intersection of a weaker secondary shock wave with the initial expanding shock wave. (Image credit: Defense Research and Development Canada; via io9)
4th Birthday: Rogue Waves
Rogue waves—individual, isolated waves far larger than the surrounding waves—were reported for centuries by sailors. But their stories of massive walls of water appearing in the open ocean were not corroborated until 1995 when a rogue wave struck an offshore platform. How these giant waves form is still under active research, but one leading theory is that nonlinear interactions between waves allow one wave to sap energy from surrounding waves and focus it into one much larger, short-lived wave. I first learned of rogue waves during a seminar in graduate school. At the time, this idea of nonlinear focusing had only been explored in simulation, but a few years later a research group was able to demonstrate the effect in a wave tank, as shown in the video above. Wait for the end, and you’ll notice how the rogue wave that takes down the ship is much larger than its predecessors. For more on rogue waves and their mind-boggling behavior, be sure to check my previous post on the subject. (Video credit: A. Chabchoub, N. Hoffmann, and N. Akhmediev)
Harnessing Ocean Waves
Ocean waves contain substantial amounts of energy, and many projects are underway to harness them as renewable energy sources. Most of these projects use the motion caused by waves to generate electrical energy. In this example, a flexible carpet is attached to hydraulic pumps. As the waves move over the carpet, it oscillates, raising and lowering the piston of the pumps. This adds hydraulic pressure to the discharge lines that run from the wave carpet to the shore. Once on dry land, that hydraulic pressure can be converted to electrical energy. This design addresses one of the major challenges in ocean-wave-energy technologies–namely how to safely transmit power from the wave farm to the shore. (Video credit: University of California Television)
Wind and Waves Visualized
Much like the wind map we featured previously, designer Cameron Beccario’s visualizations of wind and ocean surface current data draw from near-real-time sources to create a stunning picture of fluid dynamics on a planetary scale. The number of options in terms of projections and data are really quite incredible, and you’ll want to play around to get a real sense for it. Want to see the wind and total precipitable water at 1000 hPa? Here you go. Maybe you prefer studying Pacific ocean currents. All the data are there to play with. People often wonder why weather forecasts aren’t always right, but, when you look at the scale and complexity of these flows, it’s almost a wonder that we can predict them at all. (Image credits:C. Beccario/earth; via skunkbear and io9)
Breaking Waves
Most beach-goers have probably wondered just what makes the waves coming in to shore rear up and break. The secret lies in the depths–or rather the lack thereof–beneath the waves. Far from shore, the wave’s length scale is small compared to the ocean depth, and the ocean’s bottom is effectively infinitely far away to all parts of the wave. But, as the wave rolls toward shore, the depth decreases and the ocean bottom begins to influence the wave. In the trough, the ocean bottom slows the wave. Meanwhile, the crest of the wave carries forward, rising until its height reaches 80% of the water depth, at which point it will tip over and break.(Video credit: BBC)
