The vortex of Von Kármán: Key mathematical insight into swirling, asymmetric patterns of flow.


On a clear day, between the flatter islands of Cabo Verde, the soaring peaks of Fogo, Santa Antão, and São Nicolau stand out (Cape Verde).

These three volcanic islands, the largest in the archipelago, are large enough to generate rain shadow effects on some of the islands that foster unique dry forests.

The altitude also makes these islands disturb moving air masses and clouds in ways that would probably have been appreciated by Theodore von Kárm, an accomplished mathematician, aerospace engineer, and one of the pioneers of the Jet Propulsion Laboratory.

Von Kármán vortex streets are called the tracks, a characteristic pattern that can occur when a fluid passes a large, isolated, stationary object.

When he served as an assistant to Ludwig Prandtl, a pioneering German fluid dynamics scientist, von Kármán was the first to describe the oscillating flow function in mathematical terms in 1912.

Although the first to photograph the feature was a French scientist, the main finding of von Kármán was a mathematical proof showing that staggered vortices are the most durable flow pattern such characteristics can create. “I found that only the antisymmetric arrangement can be stable, and only for a certain ratio between the distance between rows and the distance between two consecutive vortices of each row,” von Kármán wrote of the discovery later on.

The vortices, in other words, are always offset and never in a line.

This image of the swirling cloud trails was captured by the Moderate Resolution Imaging Spectroradiometer (MODIS) on NASA’s Terra satellite platform on Dec. 20, 2020.

Slightly darker than the rest of the islands, the dry forests appear.

When he made his discovery of the vortexes, von Kármán was a student at the University of Göttingen (Germany). He remained in Germany until 1930, interrupting his three years of service in the Austro-Hungarian army.

Concerned about the rise of the Nazis in Germany, von Kármán accepted an offer in 1930 to head the California Institute of Technology’s new Daniel Guggenheim Aeronautical Laboratory.

In 1958, this facility later became the Jet Propulsion Laboratory of NASA.

Lauren Dauphin’s NASA Earth Observatory image, using MODIS data from NASA EOSDIS/LANCE and GIBS/Worldview.


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