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Due to its great efficiency and maneuverability, undulatory swimming is thepredominant form of locomotion in aquatic vertebrates. A myriad of animals ofdifferent species and sizes oscillate their bodies to propel themselves inaquatic environments with swimming speed scaling as the product of the animallength by the oscillation frequency. Although frequency tuning is the primarymeans by which a swimmer selects its speed, there is no consensus on themechanisms involved. In this article, we propose scaling laws for undulatoryswimmers that relate oscillation frequency to length by taking into accountboth the biological characteristics of the muscles and the interaction of themoving swimmer with its environment. Results are supported by an extensiveliterature review including approximately 1200 individuals of differentspecies, sizes and swimming environments. We highlight a crossover in lengtharound 0.5-1 m. Below this value, the frequency can be tuned between 2-20 Hzdue to biological constraints and the interplay between slow and fast muscles.Above this value, the fluid-swimmer interaction must be taken into account andthe frequency is inversely proportional to the length of the animal. Thisapproach predicts a maximum swimming speed around 5-10 m.s$^{-1}$ for largeswimmers, consistent with the threshold to prevent bubble cavitation.

Scaling the tail beat frequency and swimming speed in underwater undulatory swimming