Measurements and modeling of swimming speed dependence on stroke frequency in scyphozoan jellyfish

Abstract: Scyphozoan jellyfish exhibit the highest locomotive efficiency in the animal kingdom making them of particular interest in fluid dynamics and bioinspired robotics. Despite this prevalent analytical models of jellyfish swimming have been based on the swimming traits of hydrozoan jellyfish which utilize jet propulsion, rather than scyphozoan jellyfish which utilize paddling propulsive methods. Additionally, while stroke frequency is a driving variable in speeds achieved by undulatory swimmers, a similar dependence has not been previously explored for jellyfish. This work investigates the relationship between stroke frequency and swimming speeds in two species of scyphozoan jellyfish, Aurelia aurita and Cassiopea xamachana. An experimental study was conducted using a biohybrid technique that controls the muscle contraction frequency of freely swimming, live jellyfish with portable, implanted microelectronics. Swimming speeds were measured from video recordings in a 2.4 m tall water tank. It was found that despite differences in their natural swimming frequencies, the Aurelia and Cassiopea displayed similar speed-frequency relationships with peak swimming speeds occurring at 0.55 +/- 0.05 Hz and 0.50 +/- 0.05 Hz respectively. The difference in natural stroke frequency displayed by scyphomedusea despite the shared relationship between swimming speed and stroke frequency in these two species, suggests that natural stroke frequency may be more related to other functions such as filter feeding, rather than locomotion. A new analytical model developed for scyphozoan, paddling jellyfish was shown to have closer agreement with the experimental results than existing models based on jet propulsion. The model demonstrated the driving factors in the relationship between swimming speed and stroke frequency to be the speed of the jellyfish bell margin and changes in body kinematics with stroke frequency.