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.)
Tag: science
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)
Air Pressure Affects Splashes
When a drop falls on a dry surface, our intuition tells us it will splash, breaking up into many smaller droplets. Yet this is not always the case. The splashing of a droplet depends on many factors, including surface roughness, viscosity, drop size, and–strangely enough–air pressure. It turns out there is a threshold air pressure below which splashing is suppressed. Instead, a drop will spread and flatten without breaking up, as shown in the video above. For contrast, here is the same fluid splashing at atmospheric pressure. This splash suppression at low pressures is observed for both low and high viscosity fluids. Although the mechanism by which gases affect splashing is still under investigation, measurements show that no significant air layer exists under the spreading droplet except near the very edges. This suggests that the splash mechanism depends on how the spreading liquid encroaches on the surrounding gas. (Video credit: S. Nagel et al.; research credit: M. Driscoll et al.)
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)
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)
The Physics of a Flying-V
New research using free-flying northern bald ibises shows that during group flights the birds’ positioning and flapping maximize aerodynamic efficiency. In flight, a bird’s wings generate wingtip vortices, just as a fixed-wing aircraft does. These vortices stretch in the bird’s wake, creating upwash in some regions and downwash in others as the bird flaps. According to theory, to maximize efficiency a trailing bird should exploit upwash and avoid downwash by flying at a 45-degree angle to its leading neighbor and matching its flapping frequency. The researchers found that, on average, this was the formation and timing the flock assumed. In situations where the birds were flying one behind the next in a straight line, the birds tended to offset their flapping by half a cycle relative to the bird ahead of them–another efficient configuration according to theory. Researchers don’t yet know how the birds track and match their neighbors; perhaps, like cyclists in a peloton, they learn by experience how to position themselves for efficiency. For more information, see the researchers’ video and paper. (Photo credit: M. Unsold; research credit: S. Portugal; via Ars Technica; submitted by M. Piedallu van Wyk)
Shooting a Bullet Through a Water Balloon
This high-speed video of a bullet fired into a water balloon shows how dramatically drag forces can affect an object. In general, drag is proportional to fluid density times an object’s velocity squared. This means that changes in velocity cause even larger changes in drag force. In this case, though, it’s not the bullet’s velocity that is its undoing. When the bullet penetrates the balloon, it transitions from moving through air to moving through water, which is 1000 times more dense. In an instant, the bullet’s drag increases by three orders of magnitude. The response is immediate: the bullet slows down so quickly that it lacks the energy to pierce the far side of the balloon. This is not the only neat fluid dynamics in the video, though. When the bullet enters the balloon, it drags air in its wake, creating an air-filled cavity in the balloon. The cavity seals near the entry point and quickly breaks up into smaller bubbles. Meanwhile, a unstable jet of water streams out of the balloon through the bullet hole, driven by hydrodynamic pressure and the constriction of the balloon. (Video credit: Keyence)
“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?
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.
Fluids Round-up – 11 January 2014
It’s a big fluids round-up today, so let’s get right to it.
- Over at txchnologist, there’s a great article on controlling combustion instabilities in rocket engines with sound.
- Quanta Magazine asks if knot theory can help unravel turbulence. (submitted by iamaponyrocket)
- SciAm takes a look at how FIFA finally got their aerodynamics right so that their video game football (soccer) balls fly correctly.
- The Smithsonian considers an important question: can you fry foods in space?
- The Navy unveiled a fantastic new facility for simulating ocean waves (via J. Ouellette)
- At SciAm, there’s a nice explanation of the polar vortex and its effects on recent freezing weather. For additional background, check out this excerpt from a presentation by meteorology professor Jennifer Francis. (via Nicholas Travers)
- Cold weather also brings a host of new viral videos; NatGeo explains some of the science behind instant snow, ice fog, and frozen bubbles. See also: our own explanation of the instant snow phenomenon.
- io9 looks at the physics of knuckleballs.
- Over at Wired, Rhett Allain questions whether dwarves should stand in floating barrels. Also on the subject of The Hobbit, here’s an analysis of fire-breathing in dragons.
- At SciAm, Kyle Hill explains how inertia lets one pour a drink toward the sky.
- SciAm reports on a manufacturing process for superhydrophobic paper.
- I don’t know what banking has to do with a pool of non-Newtonian fluids, but this Malaysian ad sure makes it look fun. (via physicsphysics and jmlinhart)
- Wired has a great write-up on the mantis shrimp, which kills its prey with cavitation.
- io9 tackles explaining one of the most vexing brain teasers in fluid dynamics, the Feynman sprinkler.
- Finally, today’s lead image comes from our friends at Think Elephants, who study elephant intelligence over in Thailand and occasionally capture the animals’ mastery of fluid dynamics. Be sure to check them out and follow them on Twitter and Facebook.
(Photo credit: Think Elephants International/R. Shoer)
