Finite Amplitude Unsteady Slender Body Theory and Experiments

A theoretical study is carried out of the potential flow about slender bodies. Several theoretical models are discussed and new developments are directed toward a finite amplitude theory where flow singularities are distributed along the body centerline, which may undergo arbitrary body motion and the body cross section is presently restricted to being circular. Guided by the example of a toroidal ring, for which simple symmetry in shape makes a highly accurate solution possible, the general theory is developed and results are given for the force and rate of work done by the fluid on the moving body. An example with application to the anguilliform mode of aquatic animal propulsion is given and compared to observations on a swimming eel (Synbranchus marmoratus). Next, an experimental investigation is discussed, where a truly three-dimensional body (modeled after a Chinook salmon) was used to examine the basic slender body assumptions. Pressure measurements were made on the model surface using a set of high sensitivity pressure transducers, and several theoretical solutions are evaluated and compared with the measured pressure distribution.