Optimal Strouhal number for swimming animals

TL;DR

This paper investigates the optimal Strouhal number for swimming animals, showing it varies across species and aligns with theoretical predictions, indicating evolutionary adaptation for efficient propulsion.

Contribution

The study combines theoretical modeling with empirical data to identify how the optimal Strouhal number varies among aquatic animals of different sizes.

Findings

Optimal St increases from 0.15 to 0.8 across species

Empirical Strouhal numbers are near the predicted optimum

Model validates the evolutionary adaptation for efficient swimming

Abstract

To evaluate the swimming performances of aquatic animals, an important dimensionless quantity is the Strouhal number, St = fA/U, with f the tail-beat frequency, A the peak-to-peak tail amplitude, and U the swimming velocity. Experiments with flapping foils have exhibited maximum propulsive efficiency in the interval 0.25 < St < 0.35 and it has been argued that animals likely evolved to swim in the same narrow interval. Using Lighthill's elongated-body theory to address undulatory propulsion, it is demonstrated here that the optimal Strouhal number increases from 0.15 to 0.8 for animals spanning from the largest cetaceans to the smallest tadpoles. To assess the validity of this model, the swimming kinematics of 53 different species of aquatic animals have been compiled from the literature and it shows that their Strouhal numbers are consistently near the predicted optimum.