When winds flow past a solitary peak, like an island in the ocean, they’re disrupted into a series of counter-rotating curls. That’s what we see here stretching to the southwest of Madeira Island. The official name for this flow is a von Karman vortex street, and it can be found anywhere from a soap film to a starship. (Image credit: J. Stevens; via NASA Earth Observatory)
Tag: von Karman vortex street
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)
Swirls of Color
These beautiful swirls show the wake downstream of a thin plate. Here water is flowing from left to right and dye introduced on the plate (upstream and unseen in the photo) curls up into vortices. The vortices in the top row rotate clockwise, while the vortices along the bottom rotate anti-clockwise. This pattern of alternating vortices is extremely common in the wakes of objects and is known as a von Karman vortex street. Similar patterns are seen in soap films, behind cylinders, in the wakes of islands, and behind spaceships. (Image credit: ONERA, archived here)
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)
Glorious Vortex Street
Satellite imagery often reveals patterns we might struggle to see from the ground. Here Gaudalupe Island off the western coast of Mexico perturbs the atmosphere into a series of vortices. Air flowing across the open ocean gets deflected around and over the rocky, volcanic island, creating a line of vortices that get shed off one side of the island, then the other. The pattern is commonly referred to as a von Karman vortex street, and it appears in the wakes of spheres and cylinders, as well as islands. The two rainbow-like bands framing the vortex street are an optical phenomenon known as a glory, which NASA Earth Observatory explains here. (Image credit: NASA Earth Observatory)
Island Wakes
One of my favorite aspects of fluid dynamics is watching how patterns repeat at all kinds of scales. The cotton-candy-colored image above is a false-color satellite image of the island Tristan da Cunha (left), a volcanic island group in the South Atlantic. The prevailing winds, oriented roughly left to right in the image, flow over the rocky island and part in a series of swirls that alternate in their direction of rotation: clockwise for the upper set and counter-clockwise for the lower ones. This pattern is called a von Karman vortex street, named for an aerodynamicist who studied the mechanism. Von Karman vortices are frequently observed in satellite images of remote islands, but they are also common behind spherical and cylindrical objects of all sizes. Sometimes they even show up in sci-fi! (Image credit: NASA Earth Observatory; submitted by Steve G.)
Vortex Wake in Quebec
These satellite images show Rupert Bay in northern Quebec. Sediment and tannins have stained the bay’s waters various shades of brown, which helps show the dynamic flows of the area. Rivers empty into the bay, but the tide appears to be coming in from the northwest as well. The flow is just right to create a wake of alternating vortices off a tiny island near the center of the bay. This pattern is known as a von Karman vortex street and often appears in the wake of spheres, cylinders, and, yes, islands. (Image credit: NASA Earth Observatory; submitted by Adam V.)
Happy 50th, Star Trek!
Today’s post is largely brought to you by the fact that I have been sick the past four days and my fiance and I have been bingeing on Star Trek Voyager. At some point, we began wondering about the sequence from 0:30-0:49 in which Voyager flies through a nebula and leaves a wake of von Karman vortices. Would a starship really leave that kind of wake in a nebula?
My first question was whether the nebula could be treated as a continuous fluid instead of a collection of particles. This is part of the continuum assumption that allows physicists to treat fluid properties like density, temperature, and velocity as well-defined quantities at all points. The continuum assumption is acceptable in flows where the Knudsen number is small. The Knudsen number is the ratio of the mean free path length to a characteristic flow length, in this case, Voyager’s size. The mean free path length is the average distance a particle travels before colliding with another particle. Nebulae are much less dense than our atmosphere, so the mean free path length is larger (~ 2 cm by my calculation) but still much smaller than Voyager’s length of 344 m. So it is reasonable to treat the nebula as a fluid.
As long as the nebula is acting like a fluid, it’s not unreasonable to see alternating vortices shed from Voyager. But are the vortices we see realistic relative to Voyager’s size and speed? Physicists use the dimensionless Strouhal number to describe oscillatory flows and vortex shedding. It’s a ratio of the vortex shedding frequency times the characteristic length to the flow’s velocity. We already know Voyager’s size, so we just need an estimate of its velocity and the number of vortices shed per second. I visually estimated these as 500 m/s and 2.5 vortices/second, respectively. That gives a Strouhal number of 0.28, very close to the value of 0.2 typically measured in the wake of a cylinder, the classical case for a von Karman vortex street.
So far Voyager’s wake is looking quite reasonable indeed. But what about its speed relative to the nebula’s speed of sound? If Voyager is moving faster than the local speed of sound, we might still see vortex shedding in the wake, but there would also be a bow shock off the ship’s leading edge. To answer this question, we need to know Voyager’s Mach number, its speed relative to the local speed of sound. After some digging through papers on nebulae, I found an equation to estimate speed of sound in a nebula (Eq 9 of Jin and Sui 2010) using the specific gas constant and temperature. Because nebulae are primarily composed of hydrogen, I approximated the nebula’s gas constant with hydrogen’s value and chose a representative temperature of 500 K (also based on Jin and Sui 2010). This gave a local speed of sound of 940 m/s, and set Voyager’s Mach number at 0.53, inside the subsonic range and well away from any shock wave formation.
Of course, these are all rough estimates and back-of-the-envelope fluid dynamics calculations, but my end conclusion is that Voyager’s vortex shedding wake through the nebula is realistic after all! (Video credit: Paramount; topic also requested by heuste11)
Happy 50th anniversary, Star Trek! Some of my earliest memories of TV are of watching TNG with my parents. Star Trek taught me that curiosity and scientific inquiry were vital and valuable, and that anyone could grow up to be a scientist, engineer, and leader. Thank you for such an inspiring and hopeful vision for humanity’s future!
And, seriously, those von Karman vortices are awesome.
Soap Film Wakes
Soap films can create remarkable flow visualizations when illuminated with monochromatic (single color) light. Each of the photos above shows a flow moving from left to right with a small object near the left creating an obstruction. In the top two images, the objects are cylinders; in the lower one it’s a flat plate tilted at 45 degrees. All of the objects shed vortices as the flow moves past. These vortices alternate in direction – the first spins clockwise, the next counter-clockwise, then clockwise again and so on. This pattern is known as a von Karman vortex street and can even show up in the atmosphere! (Image credit: D. Araya et al.)
Vortices in the Wind
Heard Island, a remote patch of rock in the southwestern Indian Ocean, peeks its head above the marine cloud layer. The volcanic island disrupts the atmosphere enough to generate a von Karman vortex street, a line of alternating vortices shedding from either side of the island. Usually these vortices would march in a straight line downstream from their source. But here strong winds from the south have blown a bunch of its vortices northward, creating an unusual kink in the island’s wake. (Image credit: J. Schmaltz/LANCE EOSDIS Rapid Response; via NASA Earth Observatory)
