Paddling motion of a free-swimming jellyfish and Lagrangian coherent structure analysis

Abstract

Swimming and prey capture by prolate and oblate jellyfishes are numerically examined in two-dimensions using multi-relaxation-time lattice Boltzmann (MRT-LB) and immersed boundary (IB) methods. The near-field fluid structure interaction (FSI) and predator-prey interaction mechanisms are revealed via the simulated Eulerian flow characteristics, finite-time Lyapunov exponent (FTLE) field, and Lagrangian coherent structures (LCS). We implement appropriate periodic body force (Fb) distribution at nodal points of the elastic bell in radial direction to model the paddled swimming as well as complex feeding behavior. For a paddling jellyfish the evolved starting and stopping vortices, as move close to each other in near-wake, create the necessary vortex induced thrust that facilitate the forward body motion. The forced bell contraction in power stroke assists quicker propulsive swimming, whereas passive bell expansion in resting phase facilitates the continued vortex induced forward movement for larger duration, via the refilled fluid momentum. For feeding the detailed prey interception and precise capture areas for various jellyfish models are identified hereby via the computed prey tracks, forward and backward time FTLE fields, and LCS. Swimming performances are analyzed based on interactive thrust and drag forces, input power (energy rate required for bell contraction), output power (thrust multiplied by centroid velocity), and cost of transport (COT). At low Reynolds number (Re) the COT becomes higher for an oblate jellyfish than that of a prolate one; while with increased Re the oblate species appears more economical. However, for enhanced paddling force (Fb) or reduced flapping frequency of bell, the COT for an oblate jellyfish steadily decreases. Hereby impacts of the varied force duration, flapping amplitude, flapping frequency, and bell-elasticity on the swimming are analyzed in greater detail. Notably, the propulsion efficiency increased for higher flapping frequency. The present numerical model efficiently unfolds prey capture mechanisms that are adopted by prolate and oblate medusae and quantifies their success rate (clearance rate, CR) in prey capture. Unlike in past studies, the FTLE fields and LCS that are computed here by tracking the transient motion of a large number of suspended Lagrangian prey particles exhibit the realistic predator-prey interaction and precise prey capture surface, which are difficult to measure or analyze empirically.