Swimming of the semi-infinite strip revisited

Idealized mathematical models have been devised over the years for study of the fundamentals of the swimming of fishes. The two-dimensional flexible strip propelled by execution of transverse traveling-wave undulation is one of the most well-studied of the simple models. This model is redeveloped here, with the finding that higher propulsive efficiencies are theoretically available within the undulatory swimming mode than have been previously exposed. This is by configuring the displacement wave-form for continuously zero circulation over the body length with time, and thereby avoiding the shedding of a vortex wake and its attendant induced drag. The thrust is reactive, via acceleration processes, rather than inductive via relative velocity and lift. As in most of the classical work on fish propulsion, the analysis assumes high Reynolds number and a thin boundary layer, which provides the use of ideal-flow theory. The advance speed is assumed constant and the analysis is initially linearized, but both nonlinear and linear transient analysis are provided in supporting the basic “wakeless swimming” possibility.