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Scallops and Erosion
Although we often think of solids as immovable in the face of flow, the motion of air and water sculpts many parts of our world. One common pattern, seen both on surfaces that melt and those that dissolve into a flow, is called scalloping. Mathematical analysis shows that flat surfaces exposed to a flow that melts or dissolves them unavoidably develop these scallops. The surface becomes rougher as the scallops form, but the instability that drives them only works up to a specific level of roughness. Instead of the scallops becoming deeper and deeper, the flow shifts as the surface changes. Peaks in the surface erode faster than the valleys, which tends to keep the scallops relatively uniform in depth after they’ve formed. Scallops like these are often seen in soluble rocks like limestone or marble as well as in snow and ice. (Image credit: Seattle Times, G. Smith; research credit: P. Claudin et al., L. Ristroph)
January 31, 2018
In the Eye of a Hurricane
Although eyes are common at the center of large-scale cyclones, scientists are only now beginning to understand how they form. Since real-world cyclogenesis is complicated by many competing effects, researchers look at simplified model systems first. A typical one uses a shallow, rotating cylindrical domain in which heat rises from below. The rotation provides a Coriolis force, which shapes the flow. In particular, it causes a boundary layer along the lower surface of the domain, creating a thin region where the flow moves radially inward. (Its opposite forms at the upper surface of the domain, sending flow radiating outward.) Like an ice skater spinning, the flow’s vorticity intensifies as it approaches the central axis of rotation. When the conditions are right, this intensely swirling boundary layer flow lifts up into the main flow, forming an eyewall. The eye itself, it turns out, is merely a reaction to the eyewall’s formation. (Image credit: S. Cristoforetti/ESA; research credit: L. Oruba et al.)
January 29, 2018
Jumping Larvae
Gall midge larvae, despite their lack of legs, are prodigious jumpers. These worm-like creatures use hydrostatic pressure to jump more than 30 body lengths. To do so, the larva curls itself into a loop, latching its mouth to its tail. It then shifts the fluids inside its body, flattening itself as the pressure builds. When the larva releases its tail, it flies into the air at about 1 m/s. The human equivalent of a gall midge larva’s jump would be about 60 meters, far beyond the world record long jump of less than 9 meters (with a running start). The larva’s technique is a relatively simple but highly effective one that might be useful in applications like soft robotics. (Video credit: Science; research credit: G. Farley et al.)
January 26, 2018
An Armored Bed
A river’s flow constantly changes its underlying bed. The rocks and particulates beneath a flowing river can typically be divided into two zones: an upper layer called the bed-load zone where the flow moves particles with it and a lower layer where particles are mostly trapped but may creep over long periods. In gravelly river-beds this upper bed-load zone tends to accumulate more large particles, a phenomenon known as armoring. Experiments show that, in this region, large particles have a net vertical velocity moving upward, while smaller particles tend to move downward. Exactly why large particles are more prevalent in the bed-load zone in unknown; several theories have been offered. One suggests that the size segregation is similar to the Brazil nut effect and that smaller particles have a tendency to fall into gaps and sink more easily than larger ones. (Image and research credit: B. Ferdowsi et al., source)
January 23, 2018
Juno’s Citizen Science
The Juno mission’s JunoCam has been producing stunning photos each time the spacecraft swoops past Jupiter. The instrument has a planning team, but its primary use is for citizen scientists, who have been suggesting images to take each orbit and have been processing those images. Most of the photos we see are like the one on the left above – photos that have been heavily color-enhanced to highlight details. The image on the right shows what Jupiter would look like to the human eye. Look closely, and you’ll catch many of the same colors and shapes in both photos.
At a recent conference, a member of JunoCam’s team presented scientific results that have come from the instrument, including analysis of Jupiter’s polar storm systems (8 vortices for the north pole and 5 for the south), tantalizing hints at Jovian equivalents to earthly cloud types, and more. She also announced a new Analysis page where members of the public can both see the science in progress and participate first-hand! (Image credit: NASA / SwRI / MSSS / G. Eichstädt / S. Doran; NASA / JPL-Caltech / SwRI / MSSS / B. Jónsson; via E. Lakdawalla; submitted by jshoer)
January 22, 2018
Water Atop Oil
At first glance, this image looks much like the impact of any drop on a pool of the same liquid, but that’s not what you’re seeing. This is the impact of a water droplet on a thin film of oil, and the immiscibility of those two fluids has important effects on the collision. When the water drop impacts, it spreads and forms a compound crown that rises out of the fluid. Eventually, that momentum runs out and the crown falls into the liquid.
Water’s intermolecular forces are strong enough to pull the remains of the droplet back in on itself. As that fluid collides at the center, it gets forced up into a central jet with enough energy to eject a droplet or two at its tip. Even though this looks like a Worthington jet, it’s not. Worthington jets form after the collapse of a cavity in the impacted liquid – in other words, they form on pools, not on films. Despite the visual similarity, this central jet is formed entirely differently! (Image and research credit: Z. Che and O. Matar, source; submitted by O. Matar)
January 17, 2018
Pilot-Wave Hydrodynamics: Resources
This is the final post in a collaborative series with FYP on pilot-wave hydrodynamics. Previous posts: 1) Introduction; 2) Chladni patterns; 3) Faraday instability; 4) Walking droplets; 5) Droplet lattices; 6) Quantum double-slit experiments; 7) Hydro single- and double-slit experiments; 8) Quantum tunneling; 9) Hydrodynamic tunneling; 10) de Broglie’s pilot-wave theory
Thanks for joining us this week as we explored nearly two centuries’ worth of scientific discoveries around vibration, fluid dynamics, and quantum mechanics. For those who’d like to learn more about these and related topics, we’ve compiled some helpful resources below.
Other Videos, Articles, and Resources by Topic
Chladni Patterns
- ANSYS, “Chladni Plates”
- Brusspup, “Amazing Resonance Experiment!”
- Kenichi Kanazawa, “Color Sound”
- Microfluidic Chladni patterns
- Nigel Stanford, “Cymatics”
- Peter Remco, “Chladni patterns in a violin plate”
- Steve Mould, “Random couscous snaps into beautiful patterns”
Faraday Instability
- FYFD, Alligators and water dancing
- FYFD, Liquid crystals vibrating on a tuning fork
- Gallery of Fluid Motion, “The Tibetan singing bowl”
- Nigel Stanford, “Cymatics”
- Slow Mo Guys, “Chinese spouting bowl in slow motion.”
Quantum Mechanics
- Workgroup Bohmian Mechanics Channel
Pilot-wave Hydrodynamics
- Dual Walkers, learn about the physics from the researchers themselves
- Gallery of Fluid Motion, “The pilot-wave dynamics of walking droplets.”
- Gallery of Fluid Motion, “Shedding light on pilot-wave phenomena.”
- The Lutetium Project, “Never-ending bouncing droplets.”
- The Lutetium Project, “Dual walkers: drops and waves.”
- Through the Wormhole, Interview with Y. Couder
- Wired, “Have we been interpreting quantum mechanics wrong this whole time?”
- Veritasium, “Is this what quantum mechanics looks like?”
Selected (Academic) Bibliography by Topic
Articles marked with an asterisk (*) are recommended for their approachability and/or broad overview of the subject.
Chladni Patterns
- (*) M. Faraday, “On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces,” 1831.
- Lord Rayleigh, “On the circulation of air observed in Kundt’s tubes, and on some allied acoustical problems,” 1884.
- H. van Gerner et al., “Air-induced inverse Chladni pattern,” 2011.
Faraday Instability
- (*) M. Faraday, “On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces,” 1831.
Pilot-wave Hydrodynamics
- Y. Couder and E. Fort, “Single-particle diffraction and interference at a macroscopic scale,” 2006.
- A. Eddi et al., “Unpredictable tunnel of a classical wave-particle association,” 2009.
- (*) Y. Couder et al., “Walking droplets: A form of wave-particle duality at macroscopic scale?”, 2010.
- J. Molacek and J. Bush, “Droplets bouncing on a vibrating bath,” 2013.
- J. Molacek and J. Bush, “Droplets walking on a vibrating bath: toward a hydrodynamic pilot-wave theory,” 2013.
- D. Harris et al., “Wave-like statistics from pilot-wave dynamics in a circular corral,” 2013.
- O. Wind-Willassen et al., “Exotic states of bouncing and walking droplets,” 2013.
- (*) J. Bush, “Pilot-wave hydrodynamics,” 2015.
- D. Harris et al., “Visualization of hydrodynamic pilot-wave phenomena,” 2016.
(Image credit: A. Labuda and J. Belina)
January 12, 2018
Pilot-Wave Hydrodynamics: Droplet Tunneling
This post is part of a collaborative series with FYP on pilot-wave hydrodynamics. Previous posts: 1) Introduction; 2) Chladni patterns; 3) Faraday instability; 4) Walking droplets; 5) Droplet lattices; 6) Quantum double-slit experiments; 7) Hydro single- and double-slit experiments; 8) Quantum tunneling
Quantum tunneling is a strange subatomic behavior that was first described to explain how alpha particles escape a nucleus during radioactive decay. Classically, a particle trapped in a well can only escape if its energy is sufficiently high, but in quantum mechanics, even a particle with lower-than-necessary energy can occasionally “tunnel” out.
To test whether hydrodynamic walkers can tunnel, researchers built corrals. In the central region, the pool on which the walker moves is relatively deep. Over the walls, the pool is much shallower. In this shallow area, the wave from the droplet’s bouncing decays quickly, creating a partially reflective barrier. For most collisions, the walker reflects off the barrier. Other times, apparently at random, a collision results in the walker crossing the wall and tunneling out of its well.
Over many experiments, researchers were able to construct a probabilistic view of walker tunneling. In quantum mechanics, a particle’s likelihood of tunneling out of a well depends on the particle’s energy and the well’s thickness. The analogs for a walker are velocity and barrier thickness. The thicker the barrier, the harder it is for a walker to tunnel through. Conversely, a faster walker has a higher probability of tunneling through a barrier of a given thickness. As the authors themselves observe:
“Although our experiment is foreign to the quantum world, the similarity of the observed behaviors is intriguing.” #
As we wrap up our series tomorrow, we’ll consider some of those similarities more deeply.
(Image credits: A. Eddi et al., sources)
January 11, 2018
Pilot-Wave Hydrodynamics: Slit Experiments
This post is part of a collaborative series with FYP on pilot-wave hydrodynamics. Previous entries: 1) Introduction; 2) Chladni patterns; 3) Faraday instability; 4) Walking droplets; 5) Droplet lattices; 6) Quantum double-slit experiments
In quantum mechanics, the single and double-slit experiments are foundational. They demonstrate that light and elementary particles like electrons have wave-like and particle-like properties, both of which are necessary to explain the behaviors observed. Similarly, a hydrodynamic walker consists of both a particle and a wave, so, perhaps unsurprisingly, researchers tested them in both single-slit and double-slit experiments.
When a walker passes through a single-slit (top row), it’s deflected in a seemingly random direction due to its waves interacting with the slit. But if you watch enough walkers traverse the slit, you can put together a statistical representation of where the walker will get deflected. Compare that with the results for a series of photons passing through a slit one-at-a-time, and you’ll see a remarkable match-up.
If you test the walker instead with two slits, the droplet can only pass through one slit, but its accompanying wave passes through both (bottom row). Let enough walkers through the system one-by-one, and they, like their photonic cousins, build up interference fringes that match the quantum experiment. Diffraction and interference are only a couple of the walkers’ tricks, however. In the next posts, we’ll take a look at another analog to quantum behavior: tunneling.
(Image and research credits: Couder et al., source, selected papers 1, 2; images courtesy of E. Fort)
January 10, 2018
Pilot-Wave Hydrodynamics: Walking Drops
This post is a collaborative series with FYP on pilot-wave hydrodynamics. Previous entries: 1) Introduction; 2) Chladni patterns; 3) Faraday instability
If you place a small droplet atop a vibrating pool, it will happily bounce like a kid on a trampoline. On the surface, this seems quite counterintuitive: why doesn’t the droplet coalesce with the pool? The answer: there’s a thin layer of air trapped between the droplet and the pool. If that air were squeezed out, the droplet would coalesce. But it takes a finite amount of time to drain that air layer away, even with the weight of the droplet bearing down on it. Before that drainage can happen, the vibration of the pool sends the droplet aloft again, refreshing the air layer beneath it. The droplet falls, gets caught on its air cushion, and then sent bouncing again before the air can squeeze out. If nothing disturbs the droplet, it can bounce almost indefinitely.
Droplets don’t always bounce in place, though. When forced with the right frequency and acceleration, a bouncing droplet can transition to walking. In this state, the droplet falls and strikes the pool such that it interacts with the ripple from its previous bounce. That sends the droplet aloft again but with a horizontal velocity component in addition to its vertical one. In this state, the droplet can wander about its container in a way that depends on its history or “memory” in the form of waves from its previous bounces. And this is where things start to get a bit weird – as in quantum weirdness – because now our walker consists of both a particle (droplet) and wave (ripples). The similarities between quantum behaviors and the walking droplets, the collective behavior of which is commonly referred to as “pilot-wave hydrodynamics,” are rather remarkable. In the next couple posts, we’ll take a look at some important quantum mechanical experiments and their hydrodynamic counterparts.
(Image credit: D. Harris et al., source)
January 9, 2018

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