Inertial swimmers use flexural movements to push water and
generate thrust. We quantify this dynamical process for a slender
body in a fluid by accounting for passive elasticity and hydrodynamics and active muscular force generation and proprioception.
Our coupled elastohydrodynamic model takes the form of a nonlinear eigenvalue problem for the swimming speed and locomotion gait. The solution of this problem shows that swimmers use
quantized resonant interactions with the fluid environment to
enhance speed and efficiency. Thus, a fish is like an optimized
diode that converts a prescribed alternating transverse motion to
forward motion. Our results also allow for a broad comparative
view of swimming locomotion and provide a mechanistic basis for
the empirical relation linking the swimmer’s speed U, length L, and
tail beat frequency f, given by U=L ∼ f [Bainbridge R (1958) J Exp
Biol 35:109–133]. Furthermore, we show that a simple form of
proprioceptive sensory feedback, wherein local muscle activation
is function of body curvature, suffices to drive elastic instabilities
associated with thrust production and leads to a spontaneous
swimming gait without the need for a central pattern generator.
Taken together, our results provide a simple mechanistic view of
swimming consistent with natural observations and suggest ways
to engineer artificial swimmers for optimal performance.