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A generalization of the impulse and virial theorems with an application to bubble oscillations

Published online by Cambridge University Press:  26 April 2006

Hasan N. Oguz  and
Andrea Prosperetti
Hasan N. Oguz
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
Andrea Prosperetti
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
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Abstract

In the first part of the paper it is shown that the impulse and virial theorems of inviscid incompressible fluid mechanics are special cases of a more general theorem from which an infinity of relations can be obtained. Depending on the problem, only a finite number of these relations may be independent. An application of these results is in the approximate study of the hydrodynamic interaction of bodies. As an example, in the second part of the paper, the case of two freely translating, nonlinearly pulsating bubbles is considered. It is found that in certain parameter ranges the force between the bubbles has a sign opposite to what would be expected on the basis of the linear theory of Bjerknes forces.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 218 , September 1990 , pp. 143 - 162
Copyright
© 1990 Cambridge University Press

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