Basic mathematical overview regarding swirling, asymmetric Flow patterns

December 20, 2020. (Click on the picture for high resolution images.)

On a clear day, the high peaks at Fogo, Santa Antão and São Nicolau stand out among the flatter islands of Cabo Verde (Cape Verde). These three volcanic islands, the highest in the archipelago, stand high enough to generate rain shadow effects that support unique dry forests on some of the islands.

The altitude also helps these islands disturb air masses and passing clouds in a way that Theodore von Kárm – a skilled mathematician, aerospace engineer and one of the founders of the Living Propulsion Laboratory – would surely have appreciated. The paths are called von Kármán vortex paths, a special pattern that can occur when a liquid passes a long, isolated and stationary object. In 1912 von Kármán was the first to describe oscillating flow features in mathematical terms while working as a graduate assistant for the pioneering German fluid dynamite Ludwig Prandtl.

Although a French scientist was the first to photograph the function, von Kármán’s main mirror was a mathematical proof demonstrating that oscillating vortices were the most stable flow model that such features could produce. “I have found that only antisymmetric adjustment can be stable, and only for a certain ratio of the distance between rows and the distance between two consecutive vortices of each row,” von Kármán later wrote about the discovery. In other words, the vortices are always offset and never lined up.

Moderate resolution spectroradiometry (MODIS) on NASATerra captured this image of vortex clouds on December 20, 2020. The dry forests look a little darker than the other islands.

Von Kármán was a student at the University of Göttingen (Germany) when he made his vortex penetration. He remained in Germany until 1930, with a three-year break to serve in the Austro-Hungarian army. Concerned about the rise of the Nazis in Germany, von Kármán accepted an offer to run the new Daniel Guggenheim Aeronautical Laboratory at the California Institute of Technology in 1930. This lab later became NASA’s Jet Propulsion Laboratory in 1958.

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

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