Title: Unsteady Propulsion by an Intermittent Swimming Gait,
Abstract: Inviscid computational results are presented on a self-propelled swimmer
modeled as a virtual body combined with a two-dimensional hydrofoil pitching
intermittently about its leading edge. Lighthill (1971) originally proposed
that this burst-and-coast behavior 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 form into groups
that are self-similar with the DC. 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.