Broadcasted fertilization for the reproduction of invertebrates is accomplished through a complicated interaction between spawned gametes and the surrounding flows. Most gametes encounter each other in the vicinity of the sea urchin body where unique flow structures develop, and so analysis of local flow characteristics allows us to better understand the effect of flow on the fertilization process. This study applied a Lagrangian framework based on computational fluid dynamics to estimate the fertilization rate of eggs in a range of flow velocities (0.025–0.2 m/s) and the fertilization rate was the highest at U = 0.1 m/s, which is an intermediate flow speed. Among the four classified sub-zones, such as the aboral surface, wake, substrate, and water column, fertilization occurred most frequently in the wake and substrate regions. The relationship between fertilization rate and flow structures was investigated using three parameters: 1) standardized Morisita index to quantify the pattern of gamete distribution, 2) length of the recirculation zone to specify the areas where the eggs are most frequently fertilized, and 3) integral scale to estimate the dimension of vortex structures downstream. The results of this study show that the fertilization rate is higher inside the recirculation zone, especially when strong vortex structures are observed because the flow provides a favorable condition for the gametes to aggregate and collide with each other.

用于无脊椎动物繁殖的播撒施肥是通过产卵配子与周围水流之间复杂的相互作用来完成的。大多数配子在海胆身体附近相遇，那里形成了独特的流动结构，因此对局部流动特征的分析使我们能够更好地了解流动对受精过程的影响。本研究应用基于计算流体动力学的拉格朗日框架来估计卵子在一定流速范围（0.025-0.2 m/s）下的受精率，并且受精率在U时最高。 = 0.1 m/s，这是中间流速。在上表、尾流、底质和水柱等四个分类分区中，受精发生在尾流和底质区域最为频繁。使用三个参数研究受精率和流动结构之间的关系：1）标准化Morisita指数来量化配子分布模式，2）再循环区的长度来指定卵子最常受精的区域，3）积分尺度来估计下游涡流结构的尺寸。这项研究的结果表明，再循环区内的受精率较高，特别是当观察到强涡流结构时，因为流动为配子聚集和相互碰撞提供了有利条件。