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The biomechanics of jellyfish swimming Megill, William MacDonald

Abstract

Many jellyfish produce forward thrust by ejecting a volume of water contained within their subumbrellar cavities. This behaviour is powered by a single set of muscles lining the inside of the cavity, and controlled by a simple nerve ring at the base of the mesogleal bell. Refilling is powered by strain energy stored in the deformation of the bell. Despite the apparent simplicity of the system, four gait patterns can be identified in the swimming behaviour of the hydrozoan jellyfish, Polyorchis penicillatus Eschscholz. In increasing order of activity, the behaviours are: hopping, sink-fishing, transient swimming, and resonant swimming. The first two are used in fishing, while die others are active swimming gaits. Thrust is produced in the same way in all gaits, but in the highest frequency gait, the animal can benefit from the phenomenon of resonance to produce additional thrust. The mesoglea is a fibre-reinforced mucopolysaccharide gel. The fibres have recently been identified as microfibrils made of a protein homologous to mammalian fibrillin. Most of the energy required to power the refill stroke is thought to be stored in the stretch of these microfibrils. The elastic modulus of microfibrils has been measured in other systems and found to be in the range of 0.2 to 1.1 MPa. Jellyfish microfibrils are found here to have a similar stiffness of approximately 0.40 MPa, more than enough to account for the energy necessary to refill the bell cavity. Additional energy storage is found to be available in the deformation of the mesogleal matrix itself - the stiffness of the joint mesogleal matrix is found to be approximately 130Pa, while that of the bell mesoglea is found to be approximately 352Pa. The elastic behaviour of the whole system is non-linear, both in deflation and inflation, but can be modelled as a thick-walled cylinder made of a fibre-reinforced composite material. A numerical model of this geometry is developed and used to correctly predict the observed quasi-static behaviour of a mounted jellyfish preparation. The dynamic elastic behaviour of the jellyfish bell is modelled as a non-linear oscillator. The model successfully predicts the kinematics of the mounted preparation, matching the resonant frequency using measurements and reasonable estimates of the input parameters. It makes the additional prediction that the resonant frequency should be a function of the forcing amplitude. The model and mounted preparation are found to resonate at frequencies much higher than the free-swimming animals. Once the boundary conditions are adjusted to reflect the geometry of the free-swimming animal, the effective stiffness of the bell is found to be lower, and the model then predicts a lower resonant frequency, closer to the freeswimming frequency. The swimming frequency of the jellyfish depends on the stiffness of its bell and on the mass of water entrained by its motion. During refilling, a toroidal vortex is set up as water displaced by the expanding bell wall is sucked into the bell cavity through the velum. This mass, coupled with a measurement of the damping due to hydrodynamic drag and the adjusted stiffness, is used with the nonlinear oscillator model to predict the swimming frequency of the resonant gait for Polyorchis of all sizes.

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