Efficient kinematics for jet-propelled swimming

We use vortex sheet and viscous simulations and an analytical model to search for efficient jet-propelled swimming kinematics at large Reynolds numbers (~1000 and above). We prescribe different power-law kinematics for the bell contraction and expansion. In the simulations, two types of efficient kinematics are found: a bell radius velocity which is a nearly linear function of time, and a ``burst-and-coast'' kinematics. The analytical model studies the contraction phase only, and finds that the efficiency-optimizing kinematics transition from a nearly linear bell radius velocity (similar to the numerics) for small-to-moderate output power to an exponentially-decaying bell radius velocity for large output power.