Scaling the circulation shed by a pitching panel

James H.J. Buchholz, Melissa A. Green, Alexander J. Smits

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32 Scopus citations


A new scaling parameter is developed for the circulation shed by a rigid, rectangular panel pitching periodically about its leading edge. This parameter is the product of a kinematic and a geometric component. The kinematic component describes the relationship between the mean vorticity flux from the panel surface and the panel motion. The geometric component depends on the ratio of pitching amplitude to the span of the panel. The kinematic component is developed based on the connection between the surface pressure distribution and the resulting surface vorticity flux, which are supported in a stroke-averaged sense by pressure measurements on the surface of the panel. The parameter gives a robust scaling for the total spanwise circulation shed in a half-cycle by the panel. It provides a useful predictive tool, in that it can be either complementary to the formation number or provide an alternative scaling parameter when vortex saturation and pinch-off do not occur.

Original languageEnglish (US)
Pages (from-to)591-601
Number of pages11
JournalJournal of Fluid Mechanics
StatePublished - Dec 10 2011
Externally publishedYes

Bibliographical note

Funding Information:
A.J.S. acknowledges the support of the Office of Naval Research under MURI grant number N00014-08-1-0642. J.H.J.B. acknowledges the support of the Air Force Office of Scientific Research under grant number FA9550-11-1-0019.


  • propulsion
  • swimming/flying
  • vortex shedding


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