Everyone has watched a flag flutter in the breeze, but you may not have given much thought to it. One of the earliest scientists to consider the problem was Lord Rayleigh, who wrote an aside on the mathematics of an infinite flag flapping in a paper on jets (pdf). Today researchers consider the problem in terms of fluid-solid interaction; in other words, to study a fluttering flag, you must consider both the properties of the flag – its flexibility, length, elasticity, and so on – and the properties of the fluid – air speed, viscosity, etc. The combination of these factors governs the complicated shapes taken on by a flag. The image above is a composite of several photos of a string (a 1-d flag) flapping in a flow that moves from left to right. By combining photos, the image highlights the envelope of shapes the flag takes and demonstrates at a glance just how far the flag flutters in either direction along its length. (Image credit: C. Eloy)
Tag: flags
Schooling in Soap Films
In sports, flocks of birds, and schools of fish, we’re accustomed to thinking that the followers get an aerodynamic or hydrodynamic advantage over the leaders, but this may not always be the case. Here are two flags placed one after another in a soap film flowing from top to bottom. The flags are passive, meaning that their motion is entirely dependent on the flow around them; they cannot exert any resistive force of their own. In this case, scientists observe an effect known as inverted drafting. The lead flag actually experiences less drag – by as much as 50% – than the following flag. This seems to be a result of flow around the second flag having an upstream influence on the motion of the first. (Image and research credit: L. Ristroph and J. Zhang, pdf)
Inside a Popping Bubble
Popping a soap bubble is more complicated than what the eye can see. In high-speed video, we find that the action is very directional, with the soap bubble film pulling away from the point of rupture. As it does so, waves, like those in a flapping flag, appear along the surface and strings of fluid form along the edge of the film before breaking into droplets. This video takes matters a step further, looking at what happens to air inside a bubble when it pops. Those subtle waves and strings of fluid we see in the high-speed rupture have a distinctive effect on air inside the bubble. As the film pulls away, it leaves behind a rippled, wavy surface rather than a smooth sphere of foggy air. (Video credit: Z. Pan et al.)
Flapping Flags
Sometimes structural forces and aerodynamic forces combine to produce instabilities. One of the most common and familiar examples of this, a flag flapping in the breeze, remains extremely complex to analyze and describe. The flexibility of the flag, and its small but finite resistance to bending, combine with the variability of air flow around the flag to create a fascinating dance of effects. This same aeroelastic flutter can create disastrous results for structures and aircraft. For more on the flapping flag, see Argentina and Mahadevan (2004). (Video credit: S. Morris)
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)
Drafting Flags
Wired Science has published a gallery of fluid dynamics photos and videos, several of which have been featured here previously. There’s some neat stuff there, well worth checking out. #
This image shows two flags oriented in line with a film flowing top to bottom. The second flag interrupts the wake of the first one, which reduces the drag experienced by the first flag and increases that on the second. This is called inverted drafting and occurs because the flags are passive objects that bend to every change in the flow. #
