Journal of Fluid Mechanics

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

Hasan N.  Oguz a1 and Andrea  Prosperetti a1
a1 Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA

Article author query
oguz hn   [Google Scholar] 
prosperetti a   [Google Scholar] 


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.

(Published Online April 26 2006)
(Received August 11 1989)
(Revised January 29 1990)