A meta-analysis of steady undulatory swimming

The mechanics underlying undulatory swimming are of great general interest, both to biologists and to engineers. Over the years, more data of the kinematics of undulatory swimming have been reported. At present, an integrative analysis is needed to determine which general relations hold between kinematic variables. We here perform such an analysis by means of a meta-analysis. Using data of 27 species, we examine the relationships between the swimming speed and several kinematic variables, namely frequency and amplitude of the tail beat, length and speed of the propulsive wave, length of the body, the Reynolds number, the Strouhal number and the slip ratio U/V (between the forward swimming speed U and the rearward speed V of the propulsive wave). We present results in absolute units (cm) and in units relative to the length of the organism (total length, TL). Our data show several kinematic relations: the strongest influence on swimming speed is the speed of the propulsive wave, and the other variables (amplitude and frequency of the tail beat, length of the propulsive wave and length of the body) influence it more weakly (but significantly). In several cases, results differ when variables are expressed in different units (absolute or relative to length). Our data reveal significant differences between kinematics of swimming of shallow-bodied and deep-bodied individuals, with shallow-bodied ones swimming with a shorter propulsive wave length and a higher Strouhal number. The slip ratio U/V and the Strouhal number appear to depend on the Reynolds number in a non-linear manner.