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  • Reader Question: Lagrangian Vs. Eulerian

    Reader Question: Lagrangian Vs. Eulerian

    Reader isotropicposts writes:

    Hi, I’m taking a fluids class and I’m not sure I understand the whole lagrangian-eulerian measurements of velocity and acceleration. Could you explain this?

    This is a really great question because the Eulerian versus Lagrangian distinction is not obvious when you first learn about it. If you think about a fluid flowing, there are two sensible reference frames from which we might observe. The first is the reference frame in which we are still and the fluid rushes by. This is the Eulerian frame. It’s what you get if you stand next to a wind tunnel and watch flow pass. It’s also how many practical measurements are made. The photo above shows a Pitot tube on a stationary mount in a wind tunnel. With the air flow on, the probe measures conditions at a single stationary point while lots of different fluid particles go past.

    The other way to observe fluid motion is to follow a particular bit of fluid around and see how it evolves. This is the Lagrangian method. While this is reasonably easy to achieve in calculations and simulations, it can be harder to accomplish experimentally. To make these kinds of measurements, researchers will do things like mount a camera system to a track that runs alongside a wind tunnel at the mean speed of the flow. The resulting video will show the evolution of a specific region of flow as it moves through time and space. The video below has a nice example of this type of measurement in a wave tank. The camera runs alongside the the wave as it travels, making it possible to observe how the wave breaks.

    In the end, both reference frames contain the same physics (Einstein would not have it any other way), but sometimes one is more useful than the other in a given situation. For me, it’s easiest to think of the Eulerian frame as a laboratory-fixed frame, whereas the Lagrangian frame is one that rides alongside the fluid. I hope that helps! (Photo credit: N. Sharp; video credit: R. Liu et al.)

  • “Wallwave Vibration”

    “Wallwave Vibration”

    Loris Cecchini’s “Wallwave Vibration” series is strongly reminiscent of Faraday wave patterns. The Faraday instability occurs when a fluid interface (usually air-liquid though it can also be two immiscible liquids) is vibrated. Above a critical frequency, the flat interface becomes unstable and nonlinear standing waves form. If the excitation is strong enough, the instability can produce very chaotic behaviors, like tiny sprays of droplets or jets that shoot out like fountains. In a series of fluid-filled cells, the chaotic behaviors can even form synchronous effects above a certain vibration amplitude. (Image credit: L. Cecchini; submitted by buckitdrop)

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    Water and Aerogel

    Aerogel is an extremely light porous material formed when the liquid inside a gel is replaced with gas. When combined with water, aerogel powders can have some wild superhydrophobic effects. Here water condensed on a liquid nitrogen cooler has dripped onto a floor scattered with aerogel powder from the nitrogen’s shipping container. The result is that the water gets partially coated in aerogel powder and takes on some neat properties. Its contact angle with the surface increases – in other words, it beads up – which is typical of superhydrophobicity. When disturbed, the water breaks easily into droplets which do not immediately recombine upon contact. With sufficient distortion, they can rejoin. You can see some other neat examples of aerogel-coated water behaviors in this second video as well. (Video credit: ophilcial; submitted by Jason I.)

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    The Kaye Effect

    The Kaye effect is particular to shear-thinning non-Newtonian fluids – that is, fluids with a viscosity that decreases under deformation. The video above includes high-speed footage of the phenomenon using shampoo. When drizzled, the viscous liquid forms a heap. The incoming jet causes a dimple in the heap, and the local viscosity in this dimple drops due to the shear caused by the incoming jet. Instead of merging with the heap, the jet slips off, creating a streamer that redirects the fluid. This streamer can rise as the dimple deepens, but, in this configuration, it is unstable. Eventually, it will strike the incoming jet and collapse. It’s possible to create a stable version of the Kaye effect by directing the streamer down an incline. (Video credit: S. Lee)

  • Supernova Core Collapse

    Supernova Core Collapse

    A core-collapse, or Type II, supernova occurs in massive stars when they can no longer sustain fusion. For most of their lives, stars produce energy by fusing hydrogen into helium. Eventually, the hydrogen runs out and the core contracts until it reaches temperatures hot enough to cause the helium to fuse into carbon. This process repeats through to heavier elements, producing a pre-collapse star with onion-like layers of elements with the heaviest elements near the center. When the core consists mostly of nickel and iron, fusion will come to an end, and the core’s next collapse will trigger the supernova. When astronomers observed Supernova 1987A, the closest supernova in more than 300 years, models predicted that the onion-like layers of the supernova would persist after the explosion. But observations showed core materials reaching the surface much faster than predicted, suggesting that turbulent mixing might be carrying heavier elements outward. The images above show several time steps of a 2D simulation of this type of supernova. In the wake of the expanding shock wave, the core materials form fingers that race outward, mixing the fusion remnants. Hydrodynamically speaking, this is an example of the Richtmyer-Meshkov instability, in which a shock wave generates mixing between fluid layers of differing densities. (Image credit: K. Kifonidis et al.; see also B. Remington)

  • Freshwater Flux

    Freshwater Flux

    These satellite images show the effects of a sudden influx of warm freshwater on sea ice in the Arctic Ocean. On the left are natural color satellite images of Canada’s Mackenzie River delta where it enters the Beaufort Sea. On the right are temperature maps of the ice and water surface temperatures for the same regions. In June 2012, the coastal sea ice that had been blocking the river’s delta broke, releasing a massive discharge of river water. The natural color images show brown and tan sediment reaching far out from the river delta, but the temperature maps on the right are even more dramatic. Warmer river water has spread many hundreds of kilometers from the delta, melting sea ice and raising the open water surface temperatures by an average of 6.5 degrees Celsius. The effects of river discharge on sea ice melt are increasing as inland Arctic areas warm more in the summers and the sea ice becomes thinner and more vulnerable each year. (Image credits: NASA Earth Observatory)

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    How Dogs Drink

    This high-speed footage shows how a dog drinks. The dog’s tongue curls backwards, creating a large area of surface contact with the water. When the dog pulls its tongue back up, water adheres to it and is drawn upward in a column. The dog then closes its mouth around the water before it falls. Fundamentally, this is the same mechanism as the one cats use. Part of the reason that dogs are messier drinkers, though, is that the backwards curl of their tongue picks up extra water. Because the dog has no cheeks, there’s no way to move this water from the underside to the top of the tongue and so the water just falls back out. (Video credit: Oxford Scientific Films; submitted by Carolyn W.)

  • Dust Storm in Texas

    Dust Storm in Texas

    This aerial photo shows the leading edge of a haboob–an intense dust storm–sweeping across Texas last week. Although dust can be stirred up under many circumstances, haboobs are a specific meteorological phenomenon with winds as high as 100 kph and towering clouds of dust kilometers high. This particular storm swept through five US states last week along an incoming cold front. The winds accompanying the cold front swept up silt, dirt, and dust from the drought-ridden Southwest and carried it along to envelope towns and cities along the way. Although the term is Arabic in origin, haboobs occur throughout the world, typically at the leading edge of a cold front or thunderstorm.  (Photo credit: R. Scott)

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    Flowing Uphill

    Science Friday takes an inside look at self-propelled Leidenfrost droplets like those we’ve featured previously. The Leidenfrost effect takes place when a liquid comes in contact with a surface much, much hotter than its boiling point. Part of the liquid is vaporized, creating a thin gas layer that both insulates the remaining liquid and causes it to move with very little friction. Over a flat surface, this underlying vapor will spread in any direction. But by covering the surface with ratchets, it’s possible to direct the vapor in a particular direction, which propels the droplet in the opposite direction. Check out the video and our previous posts for more! (Video credit: Science Friday; via io9 and submitted by Urs)

  • “Demersal”

    “Demersal”

    The ethereal shapes of inks and paints falling through water make fascinating subjects. Here the ink appears to rise because the photographs are upside-down. The fluid forms mushroom-like plumes and little vortex rings. The strands that split apart into tiny lace-like fingers are an example of the Rayleigh-Taylor instability, which occurs when a denser fluid sinks into a less dense one. Similar fingering can occur on much grander scales, as well, like in the Crab Nebula. These images come from photographer Luka Klikovac’s “Demersal” series. (Photo credit: L. Klikovac)

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