Earlier this summer, the spillway of the Banja Dam was opened for the first time, releasing a stream of excess water from the reservoir. As you can see above, waves quickly formed at the surface of the falling water. You’ve likely noticed this yourself in the run-off along the street after a storm. It turns out that shallow water running down an incline is unstable. A disturbance to the flow – from surface roughness, vibration, or a change in curvature – will grow, just like a ball sitting at the top of a hill will roll down as soon as it’s prodded. For more about this kind of instability, check out this post or my video about boundary layer stability and the Space Shuttle. (Image credit: Guillaume TYTECA, source; via Gizmodo)
Tag: instability
Rayleigh-Taylor Waves
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)
HIFiRE
Earlier this month, an international team launched a successful hypersonic flight test in Australia. The Hypersonic International Research Experimentation (HIFiRE) Flight 5b was launched atop a two-stage rocket and reached its maximum speed of Mach 7.5, well above Mach 5, which defines the start of the hypersonic regime. The purpose of this particular flight test was not to test new propulsion technologies – there was no scramjet engine on this flight. Instead, researchers wanted to study aerodynamics at high Mach number, specifically the behavior of the air very close to the vehicle, its boundary layer.
The payload being tested was an elliptical cone mounted on the front of the vehicle and shown in images above. The shape of the payload is such that flow will curve around the cone rather than following straight lines. The image on the lower right contains black streamlines that show how air twists around the cone. This complex flowfield complicates the physics of the boundary layer near the cone’s surface and increases the likelihood that the boundary layer will transition from laminar flow to turbulent flow, thereby increasing heating on the payload. Ideally, the data from the test flight will let engineers test their ability to understand and predict this boundary layer transition in the future. For more on boundary layer transition and its effects at hypersonic speeds, check out my latest FYFD video. (Image credit: Australia Department of Defense, R. Kimmel et al., F. Li et al.; topic requested by Guido)
Ocean Mixing
Movement in Earth’s oceans is driven by a complicated interplay of many factors like temperature, salinity, and Earth’s rotation. Above are results from a numerical simulation of the top 100 meters of ocean contained within a 1 km x 1 km box. The colors indicate surface temperature. Two major processes create the motion we see. The first is convection, in which water at the surface releases heat to the atmosphere and cools, causing it to then sink due to its greater density. Warmer water rises to replace it. This process happens quickly and dominates the early part of the simulation where we see the puffy convection cells shown on the left animation.
A slower process is in effect as well. Because of variations in the water temperature, the density of the fluid at a given depth is not constant. We can already see that at the water surface, where the temperature (and thus density) is varying significantly. Those variations in density at the same depth combined with gravity’s tendency to shift fluids create what is known as a baroclinic instability. Put simply, this instability will cause warmer water to slide horizontally past colder water. The result is the large, spinning eddy motion seen in the animation on the right. To see how the whole system develops, check out the full video below. (Image/video credit: J. Callies)
Viscous Fingers
Viscous fingers form between air and titanium dioxide sol-gel in this photograph. The two fluids are trapped in a thin gap between glass plates – a set-up known as a Hele-Shaw cell. The dendritic fingers we see form when the less viscous air pushes into the more viscous sol-gel. This is an example of the Saffman-Taylor instability. The psychedelic colors are a result of thin-film interference and the way light interacts with very thin materials. The same effect is responsible for the colors on soap bubbles. (Image credit: C. Trease)
Crown Splash Sealing
A sphere falling into water generates a spectacular crown
splash at the surface. The object’s impact ejects a thin sheet of fluid
that rises vertically. The air pulled down into the cavity by the
sphere’s passage makes the air pressure inside the sheet lower than the
ambient air pressure on the exterior of the sheet. This pressure
difference is part of what draws the crown inward to seal the cavity. As
the splash collapses inward and seals, the liquid sheet starts to
buckle and wrinkle, leaving periodic stripes around the closing neck.
This so-called buckling instability occurs when the radius of the neck
collapses faster than the vertical speed of the splash. For more, see
the research paper or this award-winning video. (Image credit: J. Marston et al., source)
Electric Coiling
A falling jet of viscous fluid–like honey or syrup–will often coil. This happens when the jet falls quickly enough that it gets skinnier and buckles near the impact point. Triggering this coiling typically requires a jet to drop many centimeters before it will buckle. In many manufacturing situations, though, one might want a fluid to coil after a shorter drop, and that’s possible if one applies an electric field! Charging the fluid and applying an electric field accelerates the falling jet and induces coiling in a controllable manner.
An especially neat application for this technique is mixing two viscous fluids. If you’ve ever tried to mix, say, food coloring into corn syrup, you’ve probably discovered how tough it is to mix viscous substances. But by feeding two viscous fluids through a nozzle and coiling the resulting jet, researchers found that they could create a pool with concentric rings of the two liquids (see Figure C above). If you make the jet coil a lot, the space between rings becomes very small, meaning that very little molecular motion is necessary to finish mixing the fluids. (Image credits: T. Kong et al., source; via KeSimpulan)
Falling Ink
Photographer Linden Gledhill created these nebula-like composites from photos of ink diffusing in water. The work was inspired by Mark Stock’s “Spherical Rayleigh-Taylor Instabilities” series featured here last week. Like Stock’s computational art, the twisted fingers and vortex rings above form due to the denser ink falling through less dense water. The interface between the two fluids distorts under the effects of gravity and the fluids’ relative motion. Such shapes are ephemeral at best; the falling ink will quickly become turbulent and diffuse throughout the water. (Photo credit and submission: L. Gledhill)
Inside a Popping Bubble
Popping a soap bubble is more complicated than what the eye can see. In high-speed video, we find that the action is very directional, with the soap bubble film pulling away from the point of rupture. As it does so, waves, like those in a flapping flag, appear along the surface and strings of fluid form along the edge of the film before breaking into droplets. This video takes matters a step further, looking at what happens to air inside a bubble when it pops. Those subtle waves and strings of fluid we see in the high-speed rupture have a distinctive effect on air inside the bubble. As the film pulls away, it leaves behind a rippled, wavy surface rather than a smooth sphere of foggy air. (Video credit: Z. Pan et al.)
Icebergs and Caramel
What do icebergs and caramel have in common? Both have similar scalloped erosion patterns as they dissolve. When caramel dissolves in water, the denser caramel sinks in the buoyant water. An initially smooth surface will first form lines, then the flowing caramel and the uneven surface interact, forming chevrons, followed by larger scallops. A similar process happens with melting icebergs. The meltwater from an iceberg is less dense than the surrounding seawater, so it will rise as it melts. This causes variations in the salt concentration and temperature near the iceberg, which cause it to melt differently in different spots, ultimately leading to the same scallop shapes observed in the caramel. Check out the full-size PDF of the poster here. (Image credit: C. Cohen et al.)
