Soap films provide a simple and convenient method for flow visualization. Here an allen wrench swept upward through a soap film leaves a distinctive wake. This trail of counter-rotating vortices is known as a von Karman vortex street. Their spacing depends on the wrench’s size and speed. Although the von Karman vortex street is usually associated with the wake of cylinders, it shows up often in nature as well, especially in the clouds trailing rocky islands. (Photo credit: P. Nathan)
Tag: von Karman vortex street
Von Karman Vortex Streets
The wake of a cylinder is a series of alternating vortices shed as the flow moves past. This distinctive pattern is known as a von Karman vortex street. The speed of the flow and the size of the cylinder determine how often vortices are shed. Incredibly, this pattern appears at scales ranging from the laboratory demo all the way to the wakes of islands. Von Karman vortex streets can even be seen from space. (Image credit: R. Gontijo and W. Cerqueira, source video)
Island Vortex Street
Von Karman vortex streets are a pattern of alternating vortices shed in the wake of a bluff body. They’re commonly associated with cylinders and can be demonstrated in simulation and in the lab. (They even show up in supersonic flows.) But they also show up in nature quite frequently, like in this cloud pattern off Central America. Such wakes often occur downstream of rocky, volcanic islands that rise above the smooth ocean surface and disrupt the atmosphere’s boundary layer. The same phenomenon is responsible for the “singing” of electrical lines on a windy day, and I’ve even heard it make the spokes on my bicycle wheel sing in a crosswind. (Photo credit: R. Mastracchio; via @BadAstronomer; submitted by jshoer)
Cylinder Wakes
A simple cylinder in a steady flow creates a beautiful wake pattern known as a von Karman vortex street. The image above shows several examples of this pattern. Flow is from bottom to top, and the Reynolds number is increasing from left to right. In the experiment, this increasing Reynolds number corresponds to increasing the flow velocity because the cylinder size, fluid, and temperature were all fixed. As the Reynolds number first increases, the cylinder begins to shed vortices. The vortices alternate the side of the cylinder from which they are shed as well as alternating in their sense of rotation (clockwise or counterclockwise). Further increasing the Reynolds number increases the complexity of the wake, with more and more vortices being shed. The vortex street is a beautiful example of how fluid behavior is similar across a range of scales from the laboratory to our planet’s atmosphere. (Image credit: Z. Trávníček et. al)
Is the Star Trek Voyager Opening Sequence Physically Realistic?
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)
Flow Behind a Cylinder
Flow over blunt bodies produces a series of alternating vortices that are shed behind an object. The image above shows the turbulent wake of a cylinder, with flow from right to left. Red and blue dyes are used to visualize the flow. This flow structure is known as a von Karman vortex street, named for aerodynamicist Theodore von Karman. The meander of the wake is caused by the shed vortices, each of which has a rotational sense opposite its predecessor. The rapid mixing of the two dyes is a result of the flow’s turbulence. In low Reynolds number laminar cases of this flow the structure of individual vortices is more visible. Similar flow structures are seen behind islands and in the wakes of flapping objects. (Photo credit: K. Manhart et al.)
Vortex Street in the Clouds
Most objects are not particularly aerodynamic or streamlined. When air flows over such bluff bodies, they can shed regular vortices from one side and then the other. This periodic shedding creates a von Karman vortex street, like this one stretching out from Isla Socorro off western Mexico. From the wind’s perspective, the volcanic island forms a blunt disruption to the otherwise smooth ocean. This vortex shedding is seen at smaller scales, as well, in the wind tunnel, in soap films, and in water tunnels. If you’ve ever been outside on a windy day and heard the electrical lines “singing” in the wind, that’s the same phenomena, too. With the right crosswind, radial bicycle spokes will buzz for the same reason as well! (Photo credit: MODIS/NASA Earth Observatory)
Flapping Flags
The flapping of flexible objects like flags have long fascinated mankind. The figure above from Shelley and Zhang 2011 shows several possible flapping states. In (a) a thread immersed in a running soap film displays the standard von Karman vortex street of shed vortices in its wake. Parts (b) and © show the thread in coherent flapping motion; (b) shows an snapshot of the flapping thread in the soap film whereas © is a timelapse of the thread showing its full range of motion. Image (d) shows the effects of a higher flow speed–the flapping motion becomes aperiodic. Image (e) shows a stiff metal wire bent into the shape of a flapping filament; note the strong boundary layer separation around the wire compared to the thread in Image (b). As one might expect, the drag on the unflapping wire is significantly greater than the drag on the flapping thread. (Image credit: M. Shelley and J. Zhang, Shelley and Zhang 2011)
Flapping Wakes
As a flapping object moves through a fluid, many patterns of vortices can form in its wake. The familiar von Karman vortex street, so often seen in clouds or behind cylinders, is only the beginning. In the photo above, a symmetric foil flaps in a vertical soap film; as the amplitude and frequency of the oscillation varies, the wake patterns it produces change dramatically. From left to right, a) a von Karman wake; b) an inverted von Karman wake; c) a 2P wake, in which two vortex pairs are shed with each cycle; d) a 2P+2S wake, in which two vortex pairs and two single vortices are shed per cycle; e) a 4P wake; and f) a 4P+2S wake. See some of these flows in action in these videos. (Photo credit: T. Schnipper et al.)
Volcanic Vortices
The volcanoes of the South Sandwich Islands, located in the South Atlantic, have a notable effect on cloud formation in this satellite photo. Visokoi Island, on the right, sheds a wake of large vortices that distort the cloud layer above it. On the left, Zavodovski Island’s volcano does the same, with the added effect of low-level volcanic emissions, which include aerosols. These tiny particles provide a nucleus around which water droplets form, causing an marked increase in cloud formation visible in the bright tail streaming off the island. (Photo credit: NASA, via Earth Observatory)
