The Swimming of Slender Fish-Like Bodies in Waves

Abstract

In this paper the slender body theory is applied to flexible fish-like bodies. The bodies are assumed to have a constant forward velocity U normal to the crests of the waves and to move at a nearly constant depth. A flexible recoil mode is defined which is the dynamic counterpart of the stretched straight fish position defined by Lighthill (1960) for uniform flow conditions. Expressions are derived for the mean thrust and for the mean rate of working, which permit the evaluation of conditions for efficient propulsion. By adapting the motions of the body to the oncoming waves, energy can be extracted from the waves in such a way that it can be used for propulsion and braking. This phenomenon may help to explain the high speeds that cetacea are observed to sustain over long periods of time.