Abstract
In recent years studies of aquatic locomotion have provided some remarkable insights into the many features of fish swimming performances. This paper derives a scaling relation of aquatic locomotion C D(Re)2 = (Sw)2 and its corresponding log law and power law. For power scaling law, (Sw)2 = β n Re 2−1/n , which is valid within the full spectrum of the Reynolds number Re = UL/ν from low up to high, can simply be expressed as the power law of the Reynolds number Re and the swimming number Sw = ωAL/ν as Re ∝ (Sw)σ, with σ = 2 for creeping flows, σ = 4=3 for laminar flows, σ = 10=9 and σ = 14=13 for turbulent flows. For log law this paper has derived the scaling law as Sw ∝ Re=(ln Re+1:287), which is even valid for a much wider range of the Reynolds number Re. Both power and log scaling relationships link the locomotory input variables that describe the swimmer’s gait A; ω via the swimming number Sw to the locomotory output velocity U via the longitudinal Reynolds number Re, and reveal the secret input-output relationship of aquatic locomotion at different scales of the Reynolds number
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Sun, B. Scaling laws of aquatic locomotion. Sci. China Phys. Mech. Astron. 60, 104711 (2017). https://doi.org/10.1007/s11433-017-9073-1
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DOI: https://doi.org/10.1007/s11433-017-9073-1