Double Row of Vortices with Arbitrary Stagger
Published online by Cambridge University Press: 24 October 2008
Extract
The investigations of von Karman dealing with the unsymmetrical double row of vortices in an infinite sea of liquid are well known. He found that the unsymmetrical double row is stable when, and only when, cosh2πa/b = 2, where 2a is the distance between the two rows and 2b is the distance between consecutive vortices on the same row. A detailed account of the stability of the Karman street and of the symmetrical double row has been given by Lamb, and it has been shown that the symmetrical double row is unstable for all values of the ratio a/b. The object of this paper is to investigate the stability of a double row of vortices of arbitrary stagger. We define a double row of stagger 2l to be the system formed by positive vortices at the points (2nb + l, a) and negative vortices at (2mb − l, − a), where m and n assume all integral values from − ∞ to + ∞. The vortices are thus neither exactly “in step” nor exactly “out of step.” When l = 0 the system reduces to the symmetrical double row and when the system is the unsymmetrical double row.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 25 , Issue 2 , April 1929 , pp. 132 - 138
- Copyright
- Copyright © Cambridge Philosophical Society 1929
References
* Phys. Zeitschr. vol. XIII (1912), p. 53Google Scholar, and Gött. Nachr. (1912), p. 547.Google Scholar
† Hydrodynamics, 5th edn, p. 208.Google Scholar
* This result was communicated to me by Dr Jeffreys, to whom I am indebted for the suggestion giving rise to this paper.Google Scholar
* Lamb, , loc. cit.Google Scholar
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