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Structure of a linear array of hollow vortices of finite cross-section

Published online by Cambridge University Press:  29 March 2006

G. R. Baker ,
P. G. Saffman  and
J. S. Sheffield
G. R. Baker
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena
P. G. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena
J. S. Sheffield
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena
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Abstract

Free-streamline theory is employed to construct an exact steady solution for a linear array of hollow, or stagnant cored, vortices in an inviscid incompressible fluid. If each vortex has area A and the separation is L, there are two possible shapes if A½/L is less than a critical value 0.38 and none if it is larger. The stability of the shapes to two-dimensional, periodic and symmetric disturbances is considered for hollow vortices. The more deformed of the two possible shapes is found to be unstable while the less deformed shape is stable.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 74 , Issue 3 , 6 April 1976 , pp. 469 - 476
Copyright
© 1976 Cambridge University Press

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