Some Physical Mechanisms for Efficient Swimming

The central goal of this dissertation is to illustrate soe of the fundamental
physics of efficient swimming. Specifically, physical explanations are provided for two significant observations:
(a) Fish exhibit a tight range of Strouhal number, 0.2 < St < 0.4, defined as tail- beat frequency multiplied by wake width divided by swimming speed, (St = fA/U), and
(b) Most fish (such as trout, dace, goldfish, cod and dolphins) maintain constant tail-beat amplitude during cruise, and their speed is correlated linearly with their tail-beat frequency.

A computational and theoretical approach is undertaken to study the performance and wake patterns of a two-dimensional model of fish that consists of a virtual body (source of drag) connected to a pitching foil (source of thrust). The model helps elucidate the role of Strouhal number in free swimming in general, and it provides a framework for explaining the reasons behind observations (a) and (b) above. It is shown that the prevalent interpretation of St as a sufficient measure of efficiency is too broad, because Strouhal number is only a function of the shape (i.e. drag coefficient) and area of the body. In fact Strouhal number becomes effectively constant at higher speeds of swimming, and its value does not depend on the gait regardless of the
speed. This conclusion follows from showing that the thrust coefficient for the pitching foils of this study is a function of only the Strouhal number for all gaits whose amplitude is less than a certain critical value. The finding is generalized by performing a dimensional analysis, and it is shown that the variation of Strouhal number with cruising speed is simply related to the variation of the body drag coefficient with speed.

Additionally, for pitching foils, a unique optimum point is identified in the
dimensionless frequency vs. amplitude plane, where power efficiency is maximized. It is hypothesized that the better swimmers in nature are those whose body drag is matched perfectly to the thrust of their propulsor at the point of maximum efficiency of the propulsor. When so matched, the resulting swimmer will remain at its optimum power point and swim efficiently at all other speeds as well, so long as the swimmer controls its speed by maintaining fixed flap amplitude and modulating the frequency of the flap. A final goal of this work is to investigate some aspects of the hydrodynamics of batoids utilizing pectoral-fin-based propulsion. A computational study is conducted to
investigate the effect of wing planform and kinematics on the performance of a threedimensional batoid fin. Full fluid-structure interaction analysis, as well as prescribed kinematics approaches are utilized. The computational results are validated against experimental measurements.