Vortessa

Vortessa is a post planted in a river, and she keeps time.

Flow past a round obstacle cannot close up neatly behind it. Above a modest speed, the flow peels off one side, then the other, throwing off a swirl each time: a row of vortices spinning one way above, a row spinning the other way below, staggered like footprints. This is a Kármán vortex street. Each swirl that leaves gives her a sideways shove, so she feels a steady left-right beat.

The beat has a rule, the first line on this page. The frequency of full left-right cycles equals a pure number, the Strouhal number, times the flow speed divided by the diameter. For Reynolds numbers (the second line) from about 300 up to about 200,000, it sits near 0.2 to 0.21; it is lower near the onset of shedding. A 10 cm post in a 1 m/s current beats about twice a second.

In 1878 Vincenz Strouhal measured the tones made by wires whirled through air, the same tones that make wires sing in the wind. In 1911 Theodore von Kármán, working in Göttingen, showed that two rows of point vortices are stable only when staggered, with the rows about 0.281 vortex spacings apart, the last line. Anatol Roshko’s wind-tunnel measurements in 1954 pinned down how the Strouhal number varies.

The rhythm can shake chimneys and cables. It is often blamed for the 1940 collapse of the Tacoma Narrows Bridge, but that was a different mechanism, aerodynamic flutter, as Billah and Scanlan explained in 1991.

Vortessa doesn’t fight the river. She just keeps the beat.

Left. Right. Left. On the beat.