Hydromechanics and Optimization of Fast and Efficient Swimming

Abstract

This dissertation focuses on the mechanics of locomotion through a fluid medium characterized by propulsors (fins and wings) with a large aspect ratio and a large Reynolds number. The subject so delimited is of particular interest because on the order of 100 million years of animal evolution have led to fast and efficient animals converging upon such features. Idealized models of propulsors are studied in order to distill the essential physics responsible for fast and efficient locomotion, rather than the idiosyncrasies of any particular animal.

The first half considers a rigid propulsor, where the kinematics are known \textit{a priori}. We derive a set of scaling laws for the thrust, power, and efficiency of a propulsor sinusoidally heaving or pitching while translating in a uniform stream. The validity of the scaling laws is borne out by their success in collapsing a wide array of experimental data. Moreover, physical phenomena are easily attributed to different terms in the scaling laws, revealing an important but previously unappreciated interplay between added mass and lift-based forces. The scaling laws are extended to non-sinusoidal kinematics, intermittent kinematics, and combined heaving and pitching kinematics, at each step collapsing experimental data and revealing important physics.

The second half considers a flexible propulsor, where the kinematics are unknown \textit{a priori}. We start with the simplest case of a propulsor with homogeneous stiffness. To understand the role of fluid-structure resonance, we calculate the spectrum of the governing equations. The results demonstrate that resonance induces local maxima in thrust and power, in agreement with the literature, but does not by itself induce local maxima in efficiency, as assumed in the literature. Flutter eigenfunctions emerge as the system's stiffness is decreased, increasing locomotory efficiency. The results are then extended to propulsors with heterogeneous stiffness, and we calculate optimal distributions of stiffness over a wide range of conditions.

Throughout, the importance of fluid drag is discussed. For rigid propulsors, drag induces a global maximum in efficiency, plausibly explaining the narrow operating conditions observed in dolphins, sharks, bony fish, birds, bats, and insects. For flexible propulsors, drag induces local maxima in efficiency at resonance.