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  • Convective Impressionism

    Convective Impressionism

    Buoyant convection, driven by temperature-dependent changes in density, is a major force here on Earth. It’s responsible for mixing in the oceans, governs the shape of flames, and drives weather patterns. The images above show flow patterns caused by buoyant convection. The colors come from liquid crystal beads immersed in the fluid; red indicates cooler fluid and blue indicates warmer fluid. You can see plumes of warmer fluid rising in some of the photos. At the same time, though, the images are beautiful simply as art and are strongly reminiscent of works by Vincent van Gogh. (Image credit: J. Zhang et al.)

  • Wind and Waves Visualized

    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)

  • Bubble Vortices

    Bubble Vortices

    Vortices appear in scales both large and small, from your shower and the flap of an insect’s wing to cyclones and massive storms on other planets. Especially with these large-scale vortices, it can be difficult to understand the factors that affect their trajectories and intensities over time. Here researchers have studied the vortices produced on a heated half bubble for clues as to their long-term behavior. Heating the base of the bubble creates large thermal plumes which rise and generate large vortices, like the one seen above, on the bubble’s surface. Researchers observed the behavior of the vortices with and without rotation of the bubble. They found that rotating bubbles favored vortices near the polar latitudes of the bubble, just as planets like the Earth and Saturn have long-lived polar vortices. They also found that the intensification of both bubble vortices and hurricanes was reasonably captured by a single time constant, which may lead to better predictions of storm behaviors. Their latest paper is freely available here. (Image credit: H. Kellay et al.; research credit: T. Meuel et al.; via io9)

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    Inksplosion

    Chemical Bouillon are a trio of artists who use the chemistry of surface reactions to create abstract videos full of exploding and imploding droplets and colors. As chemicals react, local concentrations at the interface vary, which changes the local surface tension. These gradients drive flow from areas of low surface tension to those of higher surface tension. This is called the Marangoni effect – the same behavior that drives tears in a glass of wine. Chemical Bouillon have a whole YouTube channel dedicated to these kinds of videos, with everything from inks to ferrofluids. Be sure to take a look at some of their other videos and, if you like them, subscribe. (Video credit: Chemical Bouillon)

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    Measuring Wind Turbines with Snowfall

    One of the challenges in large-scale wind energy is that operating wind turbines do not behave exactly as predicted by simulation or wind tunnel experiments. To determine where our models and small-scale experiments are lacking, it’s useful to make measurements using a full-scale working turbine, but making quantitative measurements in such a large-scale, uncontrolled environment is very difficult. Here researchers have used natural snowfall as seeding particles for flow visualization. The regular gaps in the flow are vortices shed from the tip of the passing turbine blades. With a searchlight illuminating a 36 m x 36 m slice of the flow behind a wind turbine, the engineers performed particle image velocimetry, obtaining velocity measurements in that region that could then be correlated to the wind turbine’s power output. Such in situ measurements will help researchers improve wind turbine performance. (Video credit: J. Hong et al.)

  • Tidal Bore

    Tidal Bore

    The daily ebb and flood of the tides results from the competing forces of the Earth’s rotation and the sun and moon’s gravitational pull on the oceans. In a few areas, the local topography funnels the incoming water into a tidal bore with a distinctive leading edge. The photo above comes from the Turnagain Arm of the Cook Inlet in Alaska, where bore tides can reach a height of 7 ft and move as quickly as 15 mph. For surfers, the bore can provide a long ride–40 minutes in this case–but they can be extremely dangerous as well. Bore tides are associated with intense turbulence capable of ripping out moorings and structures; the waves are often accompanied by a roar caused by air entrainment, impact on obstacles, and the erosion of underlying sediment.  (Photo credit: S. Dickerson/Red Bull Illume; via Jennifer Ouellette)

  • Hydrodynamic Quantum Analogs

    Hydrodynamic Quantum Analogs

    Over the past few years, researchers have been exploring the dynamics of droplets bouncing on a vibrating fluid. These systems display many behaviors associated with quantum mechanics, including wave-particle duality, single-slit and double-slit diffraction, and tunneling. A new paper examines the system mathematically, showing that the droplets obey many of the same mathematics as quantum systems. In fact, the droplet-wave system behaves as a macroscopic analog of 2D quantum behaviors. The implications are intriguing, especially for teaching. Now students of quantum mechanics can experiment with a simple apparatus to understand some of the non-intuitive aspects of quantum behavior. For more, see the paper on arxiv. (Image credit: D. Harris and J. Bush; research credit: R. Brady and R. Anderson)

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    Simulating Early Planetary Impacts

    Early in our geological history, Earth was a hellish landscape of molten oceans into which metallic impactors would sometimes collide. Geophysicists have been curious how the impactors behaved after collision: did they maintain their cohesion, or did they break up into a cloud of droplets? Here the UCLA Spinlab simulates this early planetary formation by dropping liquid gallium through a tank of viscous fluid. As the video shows, the impactor’s behavior varies strongly with size. Smaller impactors stick together as a single diapir, but, as the initial size increases, the diapir becomes unstable, eventually breaking down into a cascade of droplets – a metallic rain through an ocean of magma. (Video credit: J. Wacheul et al./UCLA Spinlab; submitted by J. Aurnou)

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    “Porgrave”

    Artist Sandro Bocci uses macro imagery of fluids in his new piece “Porgrave” to create scenes reminiscent of celestial landscapes and the first moments of life. Surface tension, the Marangoni effect, and diffusion create pulsating motion in some frames whereas immiscible liquids form untouchable islands in others. “Porgrave” reminds me of work by Pery Burge and Julia Cuddy as well as sequences from films like 2001 and The Fountain, both of which created some of their effects with macro photography of fluids. Still images from “Porgrave” are available on Bocci’s site. (Video credit and submission: S. Bocci)

    ETA: This article originally misprinted the artist’s name as “Sandro Bocchi” and has been updated with the correct spelling. 

  • Solution to a Millennium Prize Problem?

    Solution to a Millennium Prize Problem?

    Reports emerged this weekend that Kazakh mathematician Mukhtarbay Otelbaev has published a proposed solution to the Navier-Stokes existence and smoothness problem, one of the seven Millennium Prize problems offered by the Clay Mathematics Institute. Today I want to explain some of the background of this problem, what is known about Otelbaev’s proposed solution, and what a solution would mean for fluid dynamics.

    The Navier Stokes Equation

    The Navier-Stokes equation is one of the governing equations of fluid dynamics and is an expression of conservation of momentum in a fluid. With the exception of a few very specific and simplified cases, there is no known general solution to equation. Instead, the equation, or a simplified model, is solved numerically using supercomputers as part of direct numerical simulation (DNS) or other forms of computational fluid dynamics (CFD). These methods allow scientists and engineers to solve the equations of fluid motion for practical problems from flow through a pipe to flow around a re-entering spacecraft.

    Existence and Smoothness

    Although the Navier-Stokes equation has been known for more than 150 years and can be solved numerically for many situations, some basic mathematical aspects of the equation have not yet been proven. For example, no one has proven that a general solution always exists in three-dimensions and that the energy of such a solution is bounded at all points. Colloquially, this is known as the Navier-Stokes existence and smoothness problem. The Clay Mathematics Institute has a very specific problem statement (PDF) asking for a proof (or counter-proof) of the existence and smoothness of the Navier-Stokes equation for an incompressible fluid in three-dimensions. Otelbaev contends that he has provided such a proof.

    Otelbaev’s Proposed Solution

    Mukhtarbay Otelbaev is an experienced mathematician with numerous papers addressing related mathematical problems. His latest paper, entitled “Existence of a strong solution to the Navier-Stokes equation,” is freely available online (PDF, in Russian, with an English abstract at the end). There is an ongoing project to translate the paper into English, and mathematicians are already evaluating the validity of this proposed solution. From what I can gather of the paper, it specifically address the Millennium Prize problem and presents Otelbaev’s proposed solution for the existence and smoothness of an incompressible fluid in three dimensions with periodic boundary conditions.

    What It Means

    As with any announcement of a major technical breakthrough, skepticism is warranted while experts evaluate the proposal. If the mathematical community upholds the validity of Otelbaev’s proof, he may be offered the Millennium Prize and other honors. More importantly, his solution could lead to a better understanding of the nature of the equation and the flows it describes. It is not, in itself, a general solution to the Navier-Stokes equation, but it may be a stepping stone in the path toward one. In the meantime, scientists and engineers will continue to rely on a combination of theory, experiment, and computation to progress our understanding of fluid dynamics.

    For More

    The story of Otelbaev’s proof and the community’s evaluation of its validity is on-going. You can follow @fyfluiddynamics and the #NavierStokes hashtag on Twitter for updates and commentary. I’d like to specially thank Catriona Stokes, Praveen C, David Sarma, and Glenn Carlson for their helpful links and observations as this story develops.

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