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  • Resources

    I get a lot of questions from people who want to learn more about fluid dynamics, whether casually or seriously. Below are some resources that may be useful in such pursuits. Affiliate links are marked with an asterisk (*).

    Videos

    • NCFMF Fluid Mechanics Series – This series of videos date from the 1960s and is intended to teach undergraduates about fluid dynamics. They remain an incredible source of demonstrations on all kinds of subjects in fluids. They feel a bit slow, but they are well worth the time.
    • Khan Academy’s Fluids series – A twelve part video series addressing some fundamentals of fluid dynamics.
    • CrashCourse Physics – If you want to dig into fluids further, it helps to know the basics. After all, the Navier-Stokes equations are simply Newton’s Laws applied to a fluid!
    • Science Off The Sphere – This video series by astronaut Don Pettit features FD and other physics in space.
    • Physics Central – Not FD-specific, but this website features lots of great educational physics, including fluid dynamics.
    • MIT + K12 – Includes fluids-related video lessons as well as many other science subjects.

    YouTube Channels

    • Library Laboratory (LIB LAB) – This project comes from fluid dynamicist A. J. Fillo. It’s aimed toward kids but is fun for all ages. Includes fluid dynamics and other topics in physics.
    • The Lutetium Project – This channel is produced by fluid dynamicists in France in conjunction with art and music students, so it offers a great intersection of art and science. Videos are available in French and English.

    Websites

    • U of Colorado’s Flow Visualization – One of my favorite websites dedicated to FD, this interdisciplinary course features engineering and art students working together to make beautiful FD. If you are at Colorado, take this course. Seriously.
    • APS Gallery of Fluid Motion – Every year the American Physical Society’s Division of Fluid Dynamics publishes the year’s best FD photos and videos. Most of this will look familiar to FYFD readers. 
    • CFD-Online – For anyone looking to get into computational fluid dynamics (CFD), this website and forum is full of great resources and comprehensive links.
    • Learn ChemE – Full of videos, screencasts, and simulations relevant to fluid dynamics.
    • Flow Visualization Facebook group – A nice place to find links to fun FD and clouds.
    • eFluids – More pretty pictures and videos from researchers.
    • opencalculus – Not directly fluids-related, but if you want to dig further into the subject, a strong foundation in math is important (see note to undergrads below).
    • Teaching Fluid Mechanics – This website focuses on demonstrations that can be used in the classroom to help teach and illustrate fluid dynamics concepts.

    Other FD Blogs

    • FlowViz – Focuses on general FD, much like FYFD does
    • Physics in Drops – Exploring the world of microfluidics
    • Liquifun – Lots of car-related aerodynamics as well as general FD
    • Symscape – Computational fluid dynamics, for the most part, but with general FD thrown in

    Books (No Diff EQ Needed)

    • An Album of Fluid Motion(*) by Milton van Dyke – This is a classic visual guide to fluid dynamics for laymen and practitioners alike.
    • The Life and Legacy of G. I. Taylor(*) by G. K. Batchelor – A great biography of one of the major fluid dynamicists of the 20th century. Taylor’s adventures range from measuring atmospheric turbulence from a ship deck to teaching himself to fly in WWI to measure pressure on a wing; from studying the swimming of microorganisms to helping predict the blast wave from the atomic bomb. Batchelor provides great insight into the man and his scientific process.
    • Life in Moving Fluids(*) by Steven Vogel – This text was written as an introduction to fluid dynamics for biologists and focuses largely on the subject’s applicability to that field. There’s some math in here, but not too much. Check out my full review.

    Books (For Those With Calculus/Diff EQ)

    • Fundamentals of Aerodynamics(*) by John Anderson – Anderson is known for textbooks (he has a bunch) that are good at introducing important concepts in fluid dynamics and aerodynamics without super-advanced mathematics and notation. This was my first aerodynamics textbook and my first introduction to the Navier-Stokes equations during my junior year.
    • Boundary Layer Theory(*) by Hermann Schlichting – Most of this text actually comes from 1930s German fluid dynamics class notes. It’s not an easy read, but it’s a great reference for advanced undergrads/early graduates working in FD.

    For Undergrads Who Want More Fluids But Don’t Know Where To Start

    In addition to the resources above, I have a couple of tips.

    • Look for professors who study fluid dynamics. – Check your school’s websites. Profs who do FD are often found in mechanical, aerospace, civil, and chemical engineering, but they can also be found in physics, mathematics, geology, atmospheric science, and theoretical and applied mechanics departments. Check out their research pages, find their office hours, and go talk to them. Volunteer to work in their lab. Demonstrate your interest!
    • Check out the NSF Research Experience for Undergraduates (NSF REU) program. Positions in this program exist all over the U.S. and frequently involve doing research over the summer. Even if your school doesn’t have anyone who does FD, you can find a school that does and do research there over the summer. (Suggestion when looking for positions: search for “fluid”, “fluid dynamics”, “fluid mechanics”, etc.) If you like it, consider graduate school!
    • Build strong mathematical skills. – One aspect of fluids education I lament is its tendency to come so late (or not at all) in a students’ education—that’s part of why FYFD exists. But the truth is that researching FD requires a lot of math—calculus, differential equations, partial differential equations, etc.—courses that get taken in freshmen and sophomore years of college before professors even start talking about FD. Having a strong foundation in these subjects is very helpful, but it’s not a prerequisite to working in a lab as an undergrad.

    Got more suggestions for helpful fluid dynamics resources? Let me know.

    (*) Links marked with an asterisk are affiliate links. Following these links and making a purchase may provide a commission to FYFD at no additional cost to you.

  • Crowds as a Fluid

    Crowds as a Fluid

    At a low density, crowds of people can behave like a fluid, which has led to numerous hydrodynamically-based crowd models. At higher densities, though, crowds are more like a soft solid, and researchers are adapting models developed for granular materials like sand to describe these crowds. In granular materials, these models help scientists identify how vibrations move through the complex network of grains and what circumstances might cause sudden reorganizations. In a large crowd, this could tell scientists the difference between the innocuous shuffle at a rock concert and the trigger for a deadly stampede. Getting real-world data for comparison is tough – obviously, it’s unethical to intentionally cause a crowd to panic – so thus far the models remain relatively untested. (Image credit: M. Lebrun; research credit: A. Bottinelli and J. Silverberg)

  • Seeing Sound

    Seeing Sound

    It’s not always easy to imagine how waves travel, but with this demonstration, you can see sound waves and how they reflect and defract. The set-up uses schlieren optics that show light and dark bands where strong changes in density take place. This, combined with a stroboscopic light, makes it possible to see the wave fronts from the acoustic transducer on the left side of the screen. Once the wave is apparent, introducing a reflective object lets us see exactly how sound waves bounce, reflect, and interfere. (Image and video credit: Harvard Natural Sciences Lecture Demonstrations)

  • Volcanic Plume

    Volcanic Plume

    Astronauts aboard the International Space Station captured this dramatic image of Raikoke Volcano’s eruption in late June. This uninhabited Pacific Island is part of the Kuril Islands off mainland Russia. The hot plume of ash and volcanic gas rose until its density matched that of the surrounding air, at which point it could only expand horizontally. This is why the plume appears to have such a flat top. It’s similar to the cumulonimbus clouds we associate with severe thunderstorms. Scientists speculate that the white ring around the plume’s base might be water vapor condensed from ambient air pulled in to the plume’s base or a side-effect of magma flowing into the surrounding sea. (Image credit: NASA; via NASA Earth Observatory)

  • Astrophysical Turbulence

    Astrophysical Turbulence

    Subsonic turbulence – like the random and chaotic motions of air and water in our everyday lives – is something we have only a limited understanding of. Our knowledge of supersonic turbulence, where shock waves and compressibility rule, is even more tenuous. In part this is because, although we can observe snapshots of supersonic turbulence in astronomical settings like the Orion Nebula shown above, we cannot watch it evolve. On these scales, features simply don’t change appreciably on human timescales.

    This has limited scientists to mostly numerical and theoretical studies of supersonic turbulence, but that is starting to change. Researchers are now building experimental set-ups that collide laser-driven plasma jets to generate boundary-free turbulence at Mach 6. Thus far, the observations are consistent with what’s been seen in nature: at low speeds, the turbulence is consistent with Kolmogorov’s theories, with energy cascading from large scales to smaller ones predictably. But as the Mach number increases, the nature of the turbulence shifts, moving toward the large density fluctuations seen in nebulae and other astrophysical realms. (Image credit: F. Battistella; research credit: T. White et al.; see also Nature Astronomy; submitted by Kam-Yung Soh)

  • Communication Between Microswimmers

    Communication Between Microswimmers

    The elongated cells of Spirostomum ambiguum swim using hair-like cilia, but when threatened, the cells contract violently, sending out long-range hydrodynamic waves, like those visualized above. Along with these waves, the cells release toxins aimed at whatever predator threatens them. In a colony, these waves act like a communication beacon. The swirl of a previous cell’s reaction tugs on its neighbors. As they contract, the message–and the toxins–spread. If the colony density is high enough, the hydrodynamic trigger waves will propagate through the entire colony, releasing enough toxins to disable even large predators. (Image and video credit: A. Mathijssen et al.)

  • What Drives Droplets

    What Drives Droplets

    There’s been a lot of interest recently in what goes on inside droplets made up of more than one fluid as they evaporate. This can be entertaining with liquids like whiskey or ouzo, but it has practical applications in ink-jet printing and manufacturing as well. And a new experiment suggests that we’ve been fundamentally wrong about what drives the flow inside these drops.

    As these drops evaporate, a donut-shaped recirculating vortex forms inside them, as seem in the cutaway views above. Conventional wisdom says that vortex is driven by surface tension. Evaporation of components like alcohol is more efficient at the edges of the drop, and as the alcohol evaporates, it creates a higher surface tension at the drop’s edge than at its peak. Marangoni forces then pull fluid down toward the edges, creating the vortex. That explanation is  consistent with observations of a sessile drop sitting on top of a surface (left side of images).

    But those observations are also consistent with another explanation: evaporating ethanol makes the local density higher, so alcohol-rich parts of the drop rise toward the peak while alcohol-poor regions sink. This difference in density would also create a flow pattern consistent with observations. So which is the real driver, surface tension or gravity?

    To find out, researchers flipped the drop upside-down (right side of images). When hanging, the preferred flow direction due to surface tension doesn’t change; flow should still go from the deepest point on the drop toward the edge. But gravity is swapped; alcohol-rich areas should be found near the edge and attachment points of the drop because buoyancy drives them there. And that is exactly what’s observed. The flow direction inside the hanging droplet is consistent with the direction prescribed by buoyancy-driven flow, thereby upending conventional wisdom. It turns out that gravity, not surface tension, is the major driver of internal flow in these multi-component droplets! (Image and research credit: A. Edwards et al.; via APS Physics; submitted by Kam-Yung Soh)

  • Sheep as a Compressible Flow

    Not everything that flows is a fluid. And when viewed from above traffic, crowds, and even herds of sheep flow in patterns like those of a fluid. In particular, these conglomerations move like compressible fluids – ones that allow substantial changes in density as they flow. From above, each sheep is just a few pixels of white, but you can see which areas of the herd have the highest density by how white an area looks. The highest density regions also tend to be the slowest moving – not surprising in a crowd.

    Now watch the gates. They act like choke points in the flow and, to some extent, like a nozzle in supersonic flow. As the sheep approach the gate, they’re in a dense, slow moving clump, but as they pass through it, the sheep speed up and spread out. This is exactly what happens in a supersonic nozzle. On the upstream end, flow in the nozzle is subsonic and dense. But once the flow hits the speed of sound at the narrowest point in the nozzle, the opening on the downstream side allows the flow to spread out and speed up past Mach 1.  (Video credit: MuzMuzTV*; submitted by Trent D.)

    *Editor’s Note: I do my best to credit the original producers of any media featured on FYFD, but this is especially difficult with viral videos as there can be many copies, all of which are uncredited. I’ve made my best guess on this one, but if this is your video, please let me know so that I can credit you properly. Thanks!

  • Replacing Kalliroscope

    Replacing Kalliroscope

    Although you may not recognize the name, you’ve probably seen Kalliroscope (top image), a pearlescent fluid that creates beautiful flow patterns when swirled. This rheoscopic fluid was invented in the mid-1960s by artist Paul Matisse and, over the following decades, became a staple of flow visualization techniques. Kalliroscope contained a suspension of crystalline guanine. Since the crystals were asymmetric, they would orient themselves depending on the flow and, from there, scatter light, creating the beautiful pearlescent effect seen above.

    Unfortunately for researchers, the production of guanine crystals was expensive and difficult. The cosmetics industry was their main consumer and over time, they moved toward mica and other cheaper mineral alternatives. The company that produced Kalliroscope gave up production in 2014, leaving researchers scrambling for a suitable alternative.

    One contender for a new standard rheoscopic fluid is based on shaving cream. By diluting shaving cream 20:1 with water, researchers are able to extract stearic acid crystals, which form an admirable alternative to Kalliroscope (middle collage). Like Kalliroscope, the resulting fluid is pearlescent and reveals flow features well (bottom two images). Stearic acid crystals are also closer in density to water than guanine, so the fluid remains in suspension far better than Kalliroscope. Plus, the best shaving cream is cheap and widely available, meaning that this is a DIY project just about anyone can do! (Image credits: Kalliroscope – P. Matisse; other images – D. Borrero-Echeverry et al.; research credit: D. Borrero-Echeverry et al.)

  • Inside a Bubble Wall

    Inside a Bubble Wall

    Schlieren photography has an almost magical feeling to it because it enables us to see the invisible – like shock waves and the tiny currents of heat that rise from our skin. But it can also reveal new perspectives on things that aren’t invisible. Here we see soap bubbles viewed through the lens of a schlieren set-up. Schlieren is sensitive to small changes in density, so instead of appearing in their usual rainbow iridescence, the bubbles look glass-like and filled with tiny currents and bubbles. What we’re seeing are some of the many tiny flow variations across the surface of a soap bubble. They’re driven by a combination of forces – gravity, temperature, and surface tension variations, to name a few. Seen in video, you can really appreciate just how dynamic a thin soap film is! (Image credit and submission: L. Gledhill, video version, more stills)

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