FYFD

Tag: instability

  • Reader Question: Rippling Runoff

    Reader Question: Rippling Runoff

    Reader junolivi asks:

    When shallow water (like runoff from melting snow) flows across pavement, it creates small repeated wave-like ripples. What creates that texture and why isn’t it just a steady flow?

    This is a great question that’s probably crossed the mind of anyone who’s seen water running down the gutter of a street after a storm. The short answer is that this gravity-driven flow is becoming unstable.

    Fluid dynamicists often like to characterize flows into two main types: laminar and turbulent. Most flows in nature are turbulent, like the wild swirls you see behind cars driving in the rain. But there are laminar flows in nature as well. Often flows that begin as laminar will become turbulent. This happens because those laminar flows are unstable to disturbances.

    The classic example of stability is a ball on a hill. If the ball is at the top of the hill and you disturb it, it will roll down the hill because its original position was unstable. If, on the other hand, the ball is in a depression, then you can prod the ball and it will eventually settle back down into its original place because that position was stable. Another way of looking at it is that, in the unstable case, the disturbance–how far the ball is from its original position–grows uncontrollably. In the stable case, on the other hand, the disturbance can be initially large but eventually decays away to nothing.

    There are many ways to disturb a laminar flow–surface roughness, vibrations, curvature, noise, etc., etc. These disturbances enter the flow and they can either grow (and become unstable) or decay (because the flow is stable to the disturbance). Just as one can look at the stability of a pendulum, one can mathematically examine the stability of a fluid flow. When one does this for water flowing down an incline, one finds that the flow is quite unstable, even in the ideal case of a pure, inviscid fluid flowing down a smooth wall.

    The reason that one sees distinctive waves with a particular wavelength (assuming that they aren’t caused by local obstructions) is directly related to this idea of instability. Essentially, the waves are the disturbance, having grown large enough to see. One could imagine that any wavelength disturbance is possible in a flow, but mathematically, what one finds, is that different wavelengths have different growth rates associated with them. The wavelength we observe is the most unstable wavelength in the flow. This is the wavelength that grows so much quicker than the others that it just overwhelms them and trips the flow to turbulence. This is very common. For example, you can see distinctive waves showing up before the flow goes turbulent in both this mixing layer simulation and this boundary layer flow.

    (Image credits: anataman, mo_cosmo; also special thanks to Garth G. who originally asked a similar question via email)

  • Featured Video Play Icon

    Behind the Science

    FYFD features lots of science, but this new video gives you a chance to see the scientists, too! It’s a behind-the-scenes look at the American Physical Society Division of Fluid Dynamics meeting that took place in San Francisco recently. You may recognize some of the stories, but I guarantee there’s new stuff, even if you were there! Special thanks to everyone who helped me make the video; I had a blast doing this. (Video credit: N. Sharp)

  • Featured Video Play Icon

    Crown Sealing

    Objects falling into a liquid pool create a beautiful splash, and, in this beautiful, award-winning video, the Splash Lab explores a peculiar instability that occurs just as the splash closes. The buckling instability they describe involves distinctive ridges that form along the splash’s ejecta sheet as it domes over and closes. The number of ridges depends both on the object size and the liquid’s properties. (Video credit: J. Marston et al.)

  • Piazza del Popolo

    Piazza del Popolo

    The lions of the fountain in Rome’s Piazza del Popolo eject a turbulent sheet of water. Random fluctuations in the water sheet cause holes to form. Driven by surface tension, these holes grow and merge, leaving behind ligaments of water which quickly break up into a spray of unevenly-sized drops. (Image credit: E. Villermaux)

  • Featured Video Play Icon

    The Rayleigh-Taylor Instability

    What’s this? An FYFD video?! Yes, at long last, I’ve begun filming some videos of my own. This first one takes a look at the Rayleigh-Taylor instability and all that action that goes on in your coffee cup. I hope to bring you more FYFD-produced videos in the future, including some videos from the American Physical Society Division of Fluid Dynamics conference in San Francisco next week. What kind of topics would you guys be interested in for the future? (Video credit: N. Sharp)

  • Momentary Crown

    Momentary Crown

    When a drop falls on a liquid film, its impact drives a thin liquid sheet called the ejecta upward and outward from the point of impact. Within  milliseconds, tiny perturbations develop in the ejecta and begin growing exponentially. These become the distinctive spikes of the crown. The momentum from the impact drives the ejecta and spikes further outward until it overcomes surface tension’s ability to hold the liquid crown together. Tiny droplets escape the crown before the ejecta comes crashing down. The whole process takes only a few hundred milliseconds from start to finish.  (Photo credit: S. Jung et al.)

  • Kelvin-Helmholtz Clouds

    Kelvin-Helmholtz Clouds

    When differing layers of fluid move past one another, friction between them causes shear. This shear quickly transforms a simple flat interface between fluid layers into a wavy unstable boundary that resembles a series of breaking ocean waves. This effect is known as the Kelvin-Helmholtz (KH) instability. In the atmosphere, this instability causes air layers with differing temperatures and moisture content to form wave-like clouds where the two layers meet. Other examples of the effect are widespread. On earth, many ocean waves are generated by wind shearing the water; elsewhere in our solar system, the cloud bands of Jupiter are lined with spinning eddies from the KH instability. (Photo credit: H. Bondo)

  • Shooting Droplets

    Shooting Droplets

    This animation shows high-speed video of a polystyrene particle striking a falling water droplet. Under the right conditions, the particle rips through the droplet, stretching the water into a bell-shaped lamella extending from a thicker rim. When the particle detaches, surface tension rapidly collapses the lamella into a ring which destabilizes. Thin ligaments and droplets fly off the crown-like ring as momentum overcomes surface tension’s ability to hold the droplet together. Be sure to check out the full video on YouTube or later next month at the APS Division of Fluid Dynamics meeting. (Yes, I will be there!) (Image credit: V. Sechenyh et al., source video)

  • Supernova Simulation

    Supernova Simulation

    New research shows that supermassive first-generation stars may explode in supernovae without leaving behind remnants like black holes. The work is a result of modeling the life and death of stars 55,000 to 56,000 times more massive than our sun. When such stars reach the end of their lives, they become unstable due to relativistic effects and begin to collapse inward. The collapse reinvigorates fusion inside the star and it begins to rapidly fuse heavier elements like oxygen, magnesium, or even iron from the helium in its core. Eventually, the energy released overcomes the binding energy of the star and it explodes outward as a supernova. The image above is a slice through such a star approximately one day after its collapse is reversed. Hydrodynamic instabilities like the Rayleigh-Taylor instability produce mixing of the heavy elements throughout the expanding interior of the star. The mixing should produce a signature that can be observed in the aftermath as these stars seed their galaxies with the heavy elements needed to form planets. For more, see Science Daily and Chen et al. (Image credit: K. Chen et al., via Science Daily; submitted by mechanicoolest)

  • Beading Fluids

    Beading Fluids

    Adding just a few polymers to a liquid can substantially change its behavior. The presence of polymers turns otherwise Newtonian fluids like water into viscoelastic fluids. When deformed, viscoelastic fluids have a response that is part viscous–like other fluids–and part elastic–like a rubber band that regains its initial shape. The collage above shows what happens to a thinning column of a viscoelastic fluid. Instead of breaking into a stream of droplets, the liquid forms drop connected with a thin filament, like beads on a string. In a Newtonian fluid, surface tension would tend to break off the drops at their narrowest point, but stretching the polymers in the viscoelastic fluid provides just enough normal stress to keep the filament intact. If the effect looks familiar, it may be because you’ve seen it in the mirror. Human saliva is a viscoelastic liquid! (Image credit: A. Wagner et al.)