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The dipolar field of rotating bodies in two dimensions

Published online by Cambridge University Press:  30 June 2008

STEFAN G. LLEWELLYN SMITH ,
SÉBASTIEN MICHELIN  and
D. G. CROWDY
STEFAN G. LLEWELLYN SMITH
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla CA 92093-0411, USA
SÉBASTIEN MICHELIN
Affiliation:
Department of Mechanical and Aerospace Engineering, Jacobs School of Engineering, UCSD, 9500 Gilman Drive, La Jolla CA 92093-0411, USA École Nationale Supérieure des Mines de Paris, 60–62 Boulevard Saint Michel, 75272 Paris cedex 06, France
D. G. CROWDY
Affiliation:
Department of Mathematics, MIT, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
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Abstract

The fluid velocity far from a translating body in two-dimensional irrotational flow is generally dipolar. This is a classical result. Here we ask when the dipolar component vanishes. Lamb (1945, § 126) provides symmetry conditions on the virtual mass tensor for this to be the case. We show that these conditions are not necessary and obtain the sufficient and necessary condition in terms of the shape of the body using conformal maps. Some explicit examples are constructed based on this condition.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 607 , 25 July 2008 , pp. 109 - 118
Copyright
Copyright © Cambridge University Press 2008

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References

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