Abstract
What wavelengths do undulatory swimmers use during propulsion? In this work we find that a wide range of body/caudal fin (BCF) swimmers, from larval zebrafish and herring to fully–grown eels, use specific wavelength (ratio of wavelength to tail amplitude of undulation) values that fall within a relatively narrow range. The possible emergence of this constraint is interrogated using numerical simulations of fluid–structure interaction. Based on these, it was found that there is an optimal specific wavelength (OSW) that maximizes the swimming speed and thrust generated by an undulatory swimmer. The observed values of specific wavelength for BCF animals are relatively close to this OSW. The mechanisms underlying the maximum propulsive thrust for BCF swimmers are quantified and are found to be consistent with the mechanisms hypothesized in prior work. The adherence to an optimal value of specific wavelength in most natural hydrodynamic propulsors gives rise to empirical design criteria for man–made propulsors.
Highlights
Dimensionless quantities are used to directly compare the biomechanics between systems of different scales [1]
Specific wavelength was calculated for 27 species (28 groups since distinction is made between young and adult axolotl) of steady–swimming body/caudal fin (BCF) swimmers based on data from a meta–analysis study [4]
Through analysis of undulatory swimmer data, we have shown that BCF swimmers undulate at a relatively narrow range of specific wavelength values
Summary
Dimensionless quantities are used to directly compare the biomechanics between systems of different scales [1]. The Strouhal number (St = 2fa/U, where f is the tail or wing beating frequency, 2a is the maximum tip–to–tip lateral excursion, and U is the forward speed) is a nondimensional number used to describe the kinematics of flying and swimming animals [2, 3]. It is suggested that natural selection drives animals to this range of Strouhal numbers because it maximizes propulsive efficiency (ratio of hydrodynamic power output to mechanical power input) during cruising [2, 6]. Another dimensionless number called the specific wavelength.
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