Flag Flapping

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)

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