Von Kármán vortex streets around invisible bluff bodies

Abstract

Satellite images captured during the past decade identify clearly von Kármán vortex streets in the atmosphere above certain islands in the Atlantic and Pacific Oceans. The vortex streets are visible due to the cloud formations since the latter behave as unintended tracers of the fluid motion driven by winds. Experimental as well as numerical simulation results of von Kármán vortex shedding for flow around a cylinder or other bluff body identify the latter in a certain range of Reynolds numbers. The satellite images, however, show these von Kármán vortex structures at elevations well above the ground level inviting the appealing question of where is the cylinder or the bluff body? This short paper identifies the answer to this question as the creation of Taylor–Proudman columns above the islands that are invisible until a tracer makes them detectable at a certain height above the island. The latter also provides the clarification that the flow is geostrophic at the leading order and consequently two-dimensional (i.e., variations occur in the horizontal directions with no leading order changes in the vertical direction). In addition, this paper shows that a small Rossby number is not a necessary requirement for the creation of Taylor–Proudman columns. The latter can emerge also if a certain modified Beltrami condition is satisfied even when Rossby number is not small.