Unsteady propulsion by an intermittent swimming gait

Abstract

Inviscid computational results are presented on a self-propelled swimmer modelled as a virtual body combined with a two-dimensional hydrofoil pitching intermittently about its leading edge. Lighthill (Proc. R. Soc. Lond. B, vol. 179, 1971, pp. 125–138) originally proposed that this burst-and-coast behaviour can save fish energy during swimming by taking advantage of the viscous Bone–Lighthill boundary layer thinning mechanism. Here, an additional inviscid Garrick mechanism is discovered that allows swimmers to control the ratio of their added-mass thrust-producing forces to their circulatory drag-inducing forces by decreasing their duty cycle, $DC$, of locomotion. This mechanism can save intermittent swimmers as much as 60 % of the energy it takes to swim continuously at the same speed. The inviscid energy savings are shown to increase with increasing amplitude of motion, increase with decreasing Lighthill number, $Li$, and switch to an energetic cost above continuous swimming for sufficiently low $DC$. Intermittent swimmers are observed to shed four vortices per cycle that give rise to an asymmetric time-averaged jet structure with both momentum surplus and deficit branches. In addition, previous thrust and power scaling laws of continuous self-propelled swimming are further generalized to include intermittent swimming. The key is that by averaging the thrust and power coefficients over only the bursting period then the intermittent problem can be transformed into a continuous one. Furthermore, the intermittent thrust and power scaling relations are extended to predict the mean speed and cost of transport of swimmers. By tuning a few coefficients with a handful of simulations these self-propelled relations can become predictive. In the current study, the mean speed and cost of transport are predicted to within 3 % and 18 % of their full-scale values by using these relations.