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On the periodicity of atmospheric von Kármán vortex streets

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Abstract

For over 100 years, laboratory-scale von Kármán vortex streets (VKVSs) have been one of the most studied phenomena within the field of fluid dynamics. During this period, countless publications have highlighted a number of interesting underpinnings of VKVSs; nevertheless, a universal equation for the vortex shedding frequency (\(N\)) has yet to be identified. In this study, we have investigated \(N\) for mesoscale atmospheric VKVSs and some of its dependencies through the use of realistic numerical simulations. We find that vortex shedding frequency associated with mountainous islands, generally demonstrates an inverse relationship to cross-stream obstacle length (\(L\)) at the thermal inversion height of the atmospheric boundary layer. As a secondary motive, we attempt to quantify the relationship between \(N\) and \(L\) for atmospheric VKVSs in the context of the popular Strouhal number (\(Sr\))–Reynolds number (\(Re\)) similarity theory developed through laboratory experimentation. By employing numerical simulation to document the \(Sr{-}Re\) relationship of mesoscale atmospheric VKVSs (i.e., in the extremely high \(Re\) regime) we present insight into an extended regime of the similarity theory which has been neglected in the past. In essence, we observe mesoscale VKVSs demonstrating a consistent \(Sr\) range of 0.15–0.22 while varying \(L\) (i.e, effectively varying \(Re\)).

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Notes

  1. We arrive at these values for \(Re\) based on magnitudinal analysis assuming \(\nu \approx 10^{-5}\) m\(^2\) s\(^{-1}\), \(\mathrm{O }\bigl (1\bigr ) <V<\mathrm{O }\bigl (10\bigr )\) m s\(^{-1}\), and \(\mathrm{O }\bigl (1\bigr ) <L< \mathrm{O }\bigl (100\bigr )\) km.

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Acknowledgments

The authors acknowledge financial support received from the Department of Defense AFOSR grant under award number (FA9550-12-1-0449). Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the Department of Defense. Additionally, computational resources were generously provided by the Renaissance Computing Institute of Chapel Hill, NC. Finally, the authors would like to thank Branko Kosovi c̀ , Gary Lackmann, Ákos Horváth, Kevin Mueller, and Mikhail Vorontsov for important dialogue and also Bert Holtslag for pointing out a relevant internal report by Annick Terpstra.

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  1. Department of Marine, Earth, and Atmospheric Sciences, North Carolina State University, Raleigh, NC , 27695, USA

    Christopher G. Nunalee & Sukanta Basu

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  1. Christopher G. Nunalee
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Correspondence to Christopher G. Nunalee.

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Nunalee, C.G., Basu, S. On the periodicity of atmospheric von Kármán vortex streets. Environ Fluid Mech 14, 1335–1355 (2014). https://doi.org/10.1007/s10652-014-9340-9

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