We employ a three-dimensional, nonlinear inviscid numerical method, in conjunction with experimental data from live fish and from a fish-like robotic mechanism, to establish the three-dimensional features of the flow around a fish-like body swimming in a straight line, and to identify the principal mechanisms of vorticity control employed in fish-like swimming. The computations contain no structural model for the fish and hence no recoil correction. First, we show the near-body flow structure produced by the travelling-wave undulations of the bodies of a tuna and a giant danio. As revealed in cross-sectional planes, for tuna the flow contains dominant features resembling the flow around a two-dimensional oscillating plate over most of the length of the fish body. For the giant danio, on the other hand, a mixed longitudinal-transverse structure appears along the hind part of the body. We also investigate the interaction of the body-generated vortices with the oscillating caudal fin and with tail-generated vorticity. Two distinct vorticity interaction modes are identified: the first mode results in high thrust and is generated by constructive pairing of body-generated vorticity with same-sign tail-generated vorticity, resulting in the formation of a strong thrust wake; the second corresponds to high propulsive efficiency and is generated by destructive pairing of body-generated vorticity with opposite-sign tail-generated vorticity, resulting in the formation of a weak thrust wake.
IntroductionFish locomotion offers a different paradigm of propulsion than utilized in humanengineered vehicles, employing a rhythmic unsteady motion of the body and fins. It has been shown in the literature that drag reduction and high propulsive efficiency are achievable through it. Gray (1936), in a still controversial paper, estimated that the drag on a swimming dolphin must be lower than on a towed rigid model of the dolphin body by a large factor; Lighthill (1971) used the kinematics measured in a live small fish, together with a large-amplitude slender body theory, and arrived at the opposite conclusion, i.e. that the drag on a swimming fish must be larger than on a rigidly towed fish model, by a factor of about three. Recently, precise measurements on an actively swimming robotic vehicle in the shape of a bluefin tuna show that the power needed to self-propel the robot is reduced by up to about 50% compared to the power needed to tow the robot straight-rigid (Barrett et al. 1999),