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.

中文翻译：

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Xeniid 珊瑚中的集体脉冲：第二部分 - 使用计算流体动力学确定协调脉冲是否有好处

协调运动已被证明可以提高许多生物体游泳、飞行和抽水的速度或效率。在许多刺胞动物（水母、海葵、珊瑚）中没有观察到协调脉冲，我们相应论文中考虑的类珊瑚就是这种情况。这一观察结果提出了一个问题，即 xeniid 珊瑚和一般刺胞动物是否由于缺乏水动力优势或其他原因不协调它们的脉冲行为。例如，缺乏大量感觉输入的弥漫性神经系统可能无法进行这种协调。同样，分组可能起到防御作用，而不是流动的动态作用。在本文中，浸入边界法用于量化由单个 xeniid 珊瑚息肉与一对息肉相比产生的流体的体积通量。息肉之间的距离和每个息肉之间的相位差都被考虑在内。更具体地说，珊瑚息肉驱动流体流动的完全耦合流固耦合问题使用浸入边界法的混合版本求解，其中使用有限差分求解纳维-斯托克斯方程，求解描述珊瑚的弹性方程使用有限元。我们探讨了三种可能的假设：（1）成对脉冲增加了息肉上方的向上流动，因此是有益的，（2）这些好处随息肉的脉冲相位差而变化，以及（3）这些好处随息肉之间的距离而变化. 我们发现，对于任何相位差，成对脉冲都没有实质性的流体动力学优势。每个珊瑚产生的流体体积通量也随着息肉之间距离的减小而减小。这一令人惊讶的结果与另一条具有相似行为的刺胞动物——倒置水母——的测量结果一致，在这种情况下，每只水母在成群结队时驱动的水流较少。