Coordinated movements have been shown to enhance the speed or efficiency of swimming, flying, and pumping in many organisms. Coordinated pulsing has not been observed in many cnidarians (jellyfish, anemones, corals), as is the case for the xeniid corals considered in our corresponding paper. This observation opens the question as to whether xeniid corals, and cnidarians in general, do not coordinate their pulsing behavior for lack of a hydrodynamic advantage or for other reasons. For example, a diffuse nervous system with lack of substantial sensory input may not be capable of such coordination. Similarly, grouping may serve a defensive role rather than a fluid dynamic role. In this paper, the immersed boundary method is used to quantify the volumetric flux of fluid generated by an individual xeniid coral polyp in comparison with a pair of polyps. Both the distances between the polyps and the phase difference between each polyp are considered. More specifically, the fully coupled fluid-structure interaction problem of a coral polyp driving fluid flow is solved using a hybrid version of the immersed boundary method where the Navier–Stokes equations are solved using a finite differences and the elasticity equations describing the coral are solved using finite elements. We explore three possible hypotheses: (1) pulsing in pairs increases upward flow above the polyps and is thus beneficial, (2) these benefits vary with the polyps’ pulsing phase difference, and (3) these benefits vary with the distance between the polyps. We find that there is no substantial hydrodynamic advantage to pulsing in a pair for any phase difference. The volumetric flux of fluid generated by each coral also decreases as the distance between polyps is decreased. This surprising result is consistent with measurements taken from another cnidarian with similar behavior, the upside down jellyfish, in which each medusa drives less flow when in a group.
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The authors would like to thank Boyce Griffith for the development of IBAMR, Roi Holzman and Uri Shavit for introducing us to pulsing corals and for their assistance with PIV, Shilpa Khatri for development and testing of the model and PIV, and the members of the Miller Lab who helped take care of the pulsing corals.
This work was supported by NSF PHY Grant #1504777 (to LAM) and the DFG Centre of Excellence 2117 “Centre for the Advanced Study of Collective Behaviour” (ID: 422037984). During this project, JES was supported by a Howard Hughes Medical Institute International Student Research Fellowship.
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Samson, J.E., Miller, L.A. Collective Pulsing in Xeniid Corals: Part II—Using Computational Fluid Dynamics to Determine if There are Benefits to Coordinated Pulsing. Bull Math Biol 82, 67 (2020). https://doi.org/10.1007/s11538-020-00741-y
- Collective behavior
- Fluid dynamics
- Immersed boundary method
- Biological fluid dynamics