Vortex interactions behind step cylinders with diameter ratio $D/d=2$ and 2.4 at Reynolds number ( $Re_{D}$ ) 150 were investigated by directly solving the three-dimensional Navier–Stokes equations. In accordance with previous studies, three spanwise vortex cells were captured: S-, N- and L-cell vortices. In this paper, we focused on vortex interactions between the N- and L-cell vortices, especially the vortex dislocations and subsequent formations of vortex loop structures. The phase difference accumulation process of every pair of corresponding N- and L-cell vortices and its effects on the vortex dislocations were investigated. We revealed that the total phase difference between N- and L-cell vortices was accumulated by two physically independent mechanisms, namely different shedding frequencies and different convective velocities of these two cells. The second mechanism has never been reported before. The relative importance of these two mechanisms varied periodically in the phase difference accumulation process of every pair of corresponding N- and L-cell vortices. This variation caused the vortex dislocation process and the subsequent formation of the loop structures to change from one N-cell cycle to another. Our long-time observations also revealed an interruption of the conventional antisymmetric vortex interactions between two subsequent N-cell cycles in this wake. Moreover, the trigger value and the threshold value in the phase difference accumulation processes were identified and discussed. Both values contribute to better understanding of the vortex dislocations in this kind of wake flow. Finally, the universality of our discussions and conclusions was investigated.

中文翻译：

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阶梯圆柱尾迹中的涡位错机制

通过直接求解三维 Navier-Stokes 方程，研究了雷诺数 ($Re_{D}$) 为 150 时直径比 $D/d=2$ 和 2.4 的阶梯圆柱体后面的涡流相互作用。根据先前的研究，捕获了三个展向涡旋细胞：S-、N-和 L-细胞涡旋。在本文中，我们专注于 N 和 L 细胞涡旋之间的涡旋相互作用，特别是涡旋位错和涡旋环结构的后续形成。研究了每对对应的N-和L-单元涡旋的相位差累积过程及其对涡旋位错的影响。我们发现 N 和 L 细胞涡旋之间的总相位差是由两种物理独立机制累积的，即这两个细胞的不同脱落频率和不同的对流速度。第二种机制以前从未被报道过。这两种机制的相对重要性在每对对应的 N 和 L 细胞涡旋的相位差累积过程中周期性变化。这种变化导致涡旋位错过程和随后的环结构形成从一个 N 细胞周期变为另一个。我们的长期观察还揭示了在此尾流中两个后续 N 细胞循环之间的常规反对称涡旋相互作用的中断。此外，确定和讨论了相位差累积过程中的触发值和阈值。这两个值都有助于更好地理解这种尾流中的涡旋位错。