Fuck Yeah Fluid Dynamics

Celebrating the physics of all that flows. Ask a question, submit a post idea or send an email. You can also follow FYFD on Twitter and Google+. FYFD is written by Nicole Sharp, PhD.

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Newton’s third law says that forces come in equal and opposite pairs. This means that when air exerts lift on an airplane, the airplane also exerts a downward force on the air. This is clear in the image above, which shows a an A380 prototype launched through a wall of smoke. When the model passes, air is pushed downward. The finite size of the wings also generates dramatic wingtip vortices. The high pressure air on the underside of the wings tries to slip around the wingtip to the upper surface, where the local pressure is low. This generates the spiraling vortices, which can be a significant hazard to other nearby aircraft. They are also detrimental to the airplane’s lift because they reduce the downwash of air. Most commercial aircraft today mitigate these effects using winglets which weaken the vortices’ effects. (Image credit: Nat. Geo./BBC2)

Newton’s third law says that forces come in equal and opposite pairs. This means that when air exerts lift on an airplane, the airplane also exerts a downward force on the air. This is clear in the image above, which shows a an A380 prototype launched through a wall of smoke. When the model passes, air is pushed downward. The finite size of the wings also generates dramatic wingtip vortices. The high pressure air on the underside of the wings tries to slip around the wingtip to the upper surface, where the local pressure is low. This generates the spiraling vortices, which can be a significant hazard to other nearby aircraft. They are also detrimental to the airplane’s lift because they reduce the downwash of air. Most commercial aircraft today mitigate these effects using winglets which weaken the vortices’ effects. (Image credit: Nat. Geo./BBC2)

The recently released music video for Jack White’s “High Ball Stepper” is a fantastic marriage of science and art. The audio is paired with visuals based around vibration effects using both granular materials and fluids. There are many examples of Faraday waves, the rippling patterns formed when a fluid interface becomes unstable under vibration. There are also cymatic patterns and even finger-like protrusions formed by when shear-thickening non-Newtonian fluids get agitated. (Video credit: J. White, B. Swank and J. Cathcart; submitted by Mike and Marius)

Ducks, boats, and other objects moving along water create a distinctive V-shaped pattern known as a Kelvin wake. As the boat moves, it creates disturbance waves of many different wavelengths. The constructive interference of the slower waves compresses them into the shock wave that forms either arm of the V. Sometimes evenly spaced wavelets occur along the arms as well. Between the arms are curved waves that result from other excited wave components. The pattern was first derived by Lord Kelvin as universally true at all speeds - at least for an ideal fluid - but practically speaking, water depth and propeller effects can make a difference. Recently, some physicists have even suggested that above a certain point, an object’s speed can affect the wake shape, but this remains contentious. (Image credit: K. Leidorf; via Colossal; submitted by Peter)

Last week an earthquake in Chile raised concerns over a possible tsunami in the Pacific. This animation shows a simulation of how waves would spread from the quake’s epicenter over the course of about 30 hours. In the open ocean, a tsunami wave can travel as fast as 800 kph (~500 mph), but due to its very long wavelength and small amplitude (< 1 m), such waves are almost unnoticeable to ships. It’s only near coastal areas, when the water shallows, that the wave train slows down and increases in height. Early in the video, the open ocean wave heights are only centimeters; note how, at the end of the video, the wave run-up heights along the coast are much larger, including the nearly 2 meter waves that impacted Chile. The power of the incoming waves in a tsunami are not their only danger, though; the force of the wave getting pulled back out to sea can also be incredibly destructive. (Video credit: NOAA/NWS/Pacific Tsunami Warning Center; via Wired)

The coalescence of two liquid droplets takes less than the blink of an eye, but it is the result of an intricate interplay between surface tension, viscosity, and inertia. The high-speed video above was filmed at 16000 frames per second, yet the initial coalescence of the silicone oil drops is still nearly instantaneous. At the very instant the drops meet, an infinitesimally small neck is formed between the droplets. Mathematically speaking, the pressure and curvature of the droplets diverge as a result of this tiny contact area. This is an example of a singularity. Surface tension rapidly expands the neck, sending capillary waves rippling along the drops as they become one. (Video credit: S. Nagel et al.; research credit: J. Paulsen)

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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.)

Human eyesight is not always the best for observing how nature behaves around us. Fortunately, we’ve developed cameras and sensors that allow us to effectively see in wavelengths beyond those of visible light. What’s shown here is a frying pan with a thin layer of cooking oil. To the human eye, this would be nothing special, but in the infrared, we can see Rayeigh-Benard convection cells as they form. This instability is a function of the temperature gradient across the oil layer, gravity, and surface tension. As the oil near the bottom of the pan heats up, its density decreases and buoyancy causes it to rise to the surface while cooler oil sinks to replace it. Here the center of the cells is the hot rising oil and the edges are the cooler sinking fluid. The convection cells are reasonably stable when the pan is moved, but, even if they are obscured, they will reform very quickly.  (Video credit: C. Xie)

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)

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.)

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)