A current flows past a cylinder and sheds a Kármán vortex street, simulated with vortex particles. Dye rolls up into the spirals of a smoke tunnel; drag the cylinder to move the wake.
Theodore von Kármán, 1911 · Vincenc Strouhal, 1878 · Henri Bénard, 1908
Behind a cylinder in a steady current, the flow peels away from the top and bottom in turn and rolls into vortices that drift downstream in two staggered rows, the street that Theodore von Kármán explained in 1911 (Henri Bénard had photographed it a few years before). Here it is simulated. The current flows round a cylinder kept solid by the circle theorem: every vortex has a mirror image inside the cylinder that cancels any flow through its surface.
Vortices are released from the shoulders at the rhythm Vincenc Strouhal measured in 1878, a frequency of about one fifth of the speed over the diameter, and each one moves in the flow made by all the others, so the street forms and staggers by itself. Viscosity, set by the Reynolds number, slowly spreads each vortex's core.
Below a Reynolds number of about 47 nothing is shed and the wake is two eddies trapped behind the cylinder, placed where Föppl showed in 1913 that such a pair can sit still. Above about 190 the real wake turns three-dimensional, shown here as unevenness in each release. Dye released upstream and from the cylinder rides the same flow and is drawn as streaklines, fading where it is stretched thin, as real smoke does when it is wound into a vortex core; the streamlines view draws the flow as seen moving with the street, where each vortex shows as closed loops.
Behind the mathematics
The vortex street, 1911
Hungarian-American engineer and physicist who in 1911 explained the double row of alternating vortices behind a bluff body, the Kármán vortex street, and went on to found modern aerodynamics and the Jet Propulsion Laboratory.
The shedding frequency, 1878
Czech physicist who in 1878 measured the tone of a wire singing in the wind and found its frequency set by wind speed over wire thickness, the ratio now called the Strouhal number.
