Optimality Principles of Undulatory Swimming*

A number of dimensionless quantities derived from a fish's kinematic and morphological parameters have been used to describe the hydrodynamics of swimming. In particular, body/caudal fin swimmers have been found to swim within a relatively narrow range of these quantities in nature, e.g., Strouhal number or the optimal specific wavelength. It has been hypothesized or shown that these constraints arise due to maximization of swimming speed, efficiency, or cost of transport in certain domains of this large dimensionless parameter space. Using fully resolved simulations of undulatory patterns, we investigate the existence of various optimality principles in fish swimming. Using scaling arguments, we relate various dimensionless parameters to each other. Based on these findings, we make design recommendations on how kinematic parameters for a swimming robot or vehicle should be chosen.