Kirigami is a variation of origami in which paper can be cut as well as folded. Here, researchers look at flow through a cut kirigami sheet and how that flow changes with the cuts’ length. In the top central image, white lines mark the paper boundaries. As the cut gaps get larger, flow through them transitions from a continuous jet to swirling vortex shedding. Along the bottom, we see similar patterns emerge in the wake of uniformly-cut sheets, too. On the right, the flow comes through in jets; moving leftward, it transitions to an unsteady vortex shedding flow. (Image credit: D. Caraeni and Y. Modarres-Sadeghi)
Tag: vortex shedding
Swirls Over the Canaries
Rocky, isolated islands disturb the atmosphere, sending air swirling off one side of the island and then the other. The effects are not always visible to the naked eye, but, as they do here, they can show up in satellite imagery as whirling von Karman vortex streets. The eddies of this image are due to the Canary Islands, and if you follow the line of swirls backward, you’ll find their originating islands. Note that the cloudy swirls don’t appear immediately behind the islands. That’s because there wasn’t enough moisture in the air for clouds to condense yet; the same swirls that you see in the downstream clouds exist in the clear air closer to the islands. (Image credit: A. Nussbaum; via NASA Earth Observatory)
Walking in the Wake of a Cylinder
A cylinder in a flow produces a series of alternating vortices known as a von Karman vortex street. Changing the flow speed and rotating the cylinder both allow researchers to tune the frequency of these shed vortices. What happens to an object in the wake?
For a simple hydrofoil tethered to the cylinder, the object wends back and forth along the vortices. But when that hydrofoil sits at the end of a double-pendulum, something very interesting happens. The whole apparatus follows a consistent trajectory similar to a human walking gait. Researchers are using this motion to build a robot that will help physical therapy patients regain a natural walking style. (Image and video credit: A. Carleton et al.)
Vortex Arms
A fixed cylinder will shed alternating vortices in its wake, but one allowed to oscillate forward and backward in the flow instead sheds simultaneous vortices. The shape of the wake still depends on the flow’s velocity. At low flow speeds, the two vortices are the same size when they shed. At higher velocities, the two vortices still shed simultaneously, but one will be large while the other is small. The larger vortex moves faster and travels downstream, but the smaller, slower vortex drifts inward. In the next shedding cycle, the small and large vortices switch positions, creating alternating symmetric shedding. (Image and video credit: P. Boersma et al.)
Swirls in the Wake
Rocky islands make excellent atmospheric swirls, as seen here around Guadalupe Island. Winds blowing in from the ocean get forced up and around the island’s topography, resulting in vortices that shed alternately from either side of the island. The pattern they form is known as a von Karman vortex street and is easily seen in satellite imagery, thanks to the swirls that can persist for tens of kilometers downstream. Personally, I never get tired of this one! (Image credit: NASA/GSFC/JPL; video credit: NOAA/CIRA; via Dakota Smith; submitted by @SellaTheChemist)
The Eerie Singing of the Golden Gate Bridge
Recent changes to the Golden Gate Bridge’s guardrails have created a new soundscape in the Bay Area. Under high winds, the bridge gives off an eerie, otherworldly wail that can be heard even miles away. The new guardrails are substantially thinner than the previous ones, which reduces the wind load the bridge has to endure. But that thinner profile is also what causes the noise, through a well-known phenomena known as vortex shedding.
Animation of vortex shedding behind a cylinder. (Image credit: Wikimedia) As air moves past a non-streamlined body, like a cylinder, it forms counter-rotating vortices that peel off the body at a set frequency. Fluid dynamicists use a non-dimensional number, the Strouhal number, to characterize this vortex shedding. For a simple shape like a cylinder, the Strouhal number is relatively constant, so I decided to do a quick and dirty calculation to examine the wind velocities responsible for the sound. (See also my analysis of Star Trek Voyager’s opening sequence.)
I began by collecting several videos with samples of the bridge’s singing (1, 2, 3). Then I used Adobe Audition to analyze the frequency content of the bridge noise. Below is a sample snapshot from a video taken on the bridge’s bike path, right next to the guardrail. The analysis shows three broad, but distinct peaks: a primary peak at 430 Hz, a small harmonic of that frequency at 860 Hz, and a separate, secondary peak centered at 1070 Hz. The broadness of the peaks, along with the competition between the primary and secondary peaks, is probably responsible for the disconcerting, discordant nature of the sound.
Frequency analysis of the Golden Gate Bridge’s “singing”, taken from a section of this video. (Image credit: N. Sharp) Of the other videos I analyzed, a second video from near the bridge also showed the 430 Hz peak, while a video from further away had a dominant frequency of 517 Hz. There’s a lot of uncertainty introduced in not knowing exactly when each video was filmed, but given the agreement between videos 2 and 3, I suspect that video 1’s higher frequency may be caused by interference and modulation as the sound travels.
With the major frequency in hand, I estimated the size of the new guardrail wires as 10mm in diameter. After some tweaking to adjust the Reynolds number and Strouhal numbers, that gave me an estimated wind speed of 21 meters per second, or about 47 miles per hour. That’s right in line with the 43 miles per hour discussed by the news anchors.
What if the guardrails are a little thinner? If the wires are about 7.5 mm in diameter, then it only takes winds at about 15 meters per second (34 miles per hour) to create that 430 Hz note.
Keep in mind that this analysis doesn’t predict the minimum wind speed needed to create the audible noise; all I’m able to do is a back-of-the-envelope calculation of what the likely wind speed was when a video was recorded. Nevertheless, I hope you’ll find it interesting! (Video credit: KPIX CBS News; image credits: vortex shedding – Wikimedia, frequency analysis – N. Sharp; submitted by Christina T.)
Nighttime Streets
Clouds spiral behind the islands of Tenerife and Gran Canaria in this nighttime satellite imagery. Although it’s not entirely unusual to see these von Karman vortex street clouds in the wakes of islands, this is the first time I’ve seen them at night. They form when winds off the ocean are forced up and around rocky islands. Like air moving past a cylinder, the flow forms a swirling vortex off one side of the island, which separates and moves downstream while another forms on the island’s opposite side. When the resulting flow mixes with a cloud layer, we can see the pattern from space. (Image credit: J. Stevens; via NASA Earth Observatory)
Vibrating in the Flow
Objects can obviously affect flows, but that’s not a one-way street. Flows can also affect objects, even ones as simple a circular cylinder. If you live somewhere with traffic lights mounted to a horizontal bar, you’ve probably seen this. On a windy day, the beam holding the traffic lights will oscillate up and down. This is an example of vortex-induced vibration, a coupling between the flow structures formed by an object and the motion of the object itself. With cylinders, engineers have mostly studied a situation like the traffic light – one where the motion of the cylinder is perpendicular to the direction of the flow.
But it’s also possible to get vortex-induced vibration in the same direction as the flow. That’s what you see visualized in the images above. Notice how the oscillation of the cylinders is inline with the flow direction. As with the crossflow version of vortex-induced vibration, this inline example has several wake forms that vary based on flow conditions. (Image and research credit: T. Gurian et al.)
The Tacoma Narrows Bridge
One of the most dramatic and famous engineering failures of the twentieth century is also one of the most complicated: the collapse of the Tacoma Narrows Bridge. This early suspension bridge earned the name “Galloping Gurtie” from construction workers while it was still being built because its flexibility made it prone to moving up and down under even relatively light winds. That vertical motion was due to vortex-induced vibration. As the wind blew, it shed vortices off the downstream side of the bridge. These vortices alternated, coming off the top and then bottom of the bridge deck. The resulting forces made the bridge shift up and down.
That wasn’t the bridge’s ultimate downfall, though. Shortly before it collapsed, the bridge stopped flexing up and down and instead twisted back and forth. This was a clear sign that the bridge had moved into aeroelastic flutter. In this situation, you get a feedback loop between the bridge’s aerodynamics and its structural dynamics. When the wind twists the bridge deck to a positive angle of attack, it will try to continue forcing the bridge to twist that direction. The internal forces of the bridge will try to twist it back, but when that happens, it can overshoot and end up at a negative angle of attack. At that point, the wind tries to push it further that direction and internal forces twist it back, overshooting the other way. This back-and-forth can create a dangerous feedback loop where the twisting of the bridge keeps getting worse and worse. In fact, that’s exactly what happened – right up until the bridge collapsed rather than twisting any more. (Video and image credit: Practical Engineering)
The Swimming of a Dead Fish
When I was a child, my father would take me trout fishing, and I spent hours marveling from the riverbank at the trouts’ ability to, seemingly effortlessly, hold their position in the fast-moving water. As it turns out, those trout really were swimming effortlessly, in a manner demonstrated above. The fish you see here swimming behind the obstacle is dead. There’s nothing powering it, except the energy its flexible body can extract from the flow around it.
The obstacle sheds a wake of alternating vortices into the flow, and when the fish is properly positioned in that wake, the vortices themselves flex the fish’s body such that its head and its tail point in different directions. Under just the right conditions, there’s actually a resonance between the vortices and the fish’s body that generates enough thrust to overcome the fish’s drag. This means the fish can actually swim upstream without expending any energy of its own! The researchers came across this entirely by accident, and one of the questions that remains is how the trout is able to sense its surroundings well enough to intentionally take advantage of the effect. (Image and research credit: D. Beal et al.; via PhysicsBuzz; submitted by Kam-Yung Soh)
