Aquatic vertebrate locomotion: wakes from body waves.

Abstract

Vertebrates swimming with undulations of the body and tail have inflection points where the curvature of the body changes from concave to convex or vice versa. These inflection points travel down the body at the speed of the running wave of bending. In movements with increasing amplitudes, the body rotates around the inflection points, inducing semicircular flows in the adjacent water on both sides of the body that together form proto-vortices. Like the inflection points, the proto-vortices travel towards the end of the tail. In the experiments described here, the phase relationship between the tailbeat cycle and the inflection point cycle can be used as a first approximation of the phase between the proto-vortex and the tailbeat cycle. Proto-vortices are shed at the tail as body vortices at roughly the same time as the inflection points reach the tail tip. Thus, the phase between proto-vortex shedding and tailbeat cycle determines the interaction between body and tail vortices, which are shed when the tail changes direction. The shape of the body wave is under the control of the fish and determines the position of vortex shedding relative to the mean path of motion. This, in turn, determines whether and how the body vortex interacts with the tail vortex. The shape of the wake and the contribution of the body to thrust depend on this interaction between body vortex and tail vortex. So far, we have been able to describe two types of wake. One has two vortices per tailbeat where each vortex consists of a tail vortex enhanced by a body vortex. A second, more variable, type of wake has four vortices per tailbeat: two tail vortices and two body vortices shed from the tail tip while it is moving from one extreme position to the next. The function of the second type is still enigmatic.