Efficient kinematics for jet-propelled swimming

We use computer simulations and an analytical model to study the relationship between kinematics and performance in jet-propelled jellyfish swimming. We prescribe different power-law kinematics for the bell contraction and expansion, and identify kinematics that yield high swimming speeds and/or high efficiency. In the simulations, high efficiency is found when the bell radius is a nearly linear function of time, and in a second case corresponding to ‘burst-and-coast’ kinematics. The analytical model studies the contraction phase only, and finds that the efficiency-optimizing bell radius as a function of time transitions from nearly linear (similar to the numerics) for small-to-moderate output power to exponentially decaying for large output power.