a1 Center for Atmosphere Ocean Science at the Courant Institute of Mathematical Sciences New York University, New York, NY 10012, USA
This paper presents a study of the global response of a fluid to impulsive and localized forcing; it has been motivated by the recent laboratory experiments on the locomotion of water-walking insects reported in Hu, Chan & Bush (Nature, vol. 424, 2003, p. 663). These insects create both waves and vortices by their rapid leg strokes and it has been a matter of some debate whether either form of motion predominates in the momentum budget. The main result of this paper is to argue that generically both waves and vortices are significant, and that in linear theory they take up the horizontal momentum with share 1/3 and 2/3, respectively.
This generic result, which depends only on the impulsive and localized nature of the forcing, is established using the classical linear impulse theory, with adaptations to weakly compressible flows and flows with a free surface. Additional general comments on experimental techniques for momentum measurement and on the wave emission are given and then the theory is applied in detail to water-walking insects.
Owing to its generality, this kind of result and the methods used to derive it should be applicable to a wider range of wave–vortex problems in the biolocomotion of water-walking animals and elsewhere.
(Received September 19 2005)
(Revised August 04 2006)