We have performed direct numerical simulations of flow past a tapered circular cylinder during the early transition to three dimensions for two successive taper ratios (TR) of 20 and 12.5. Our results indicate the random occurrence of vortex splits and dislocations as the topology of the shedding signature. In particular, we observe oblique cellular shedding with multiple spanwise patterns and oppositely oriented oblique cells in the shed structure. Unlike flow imposed shear, the vortex formation length becomes sensitive to the taper ratio, which removes oblique frequency waves noticed for lower shear rate. The local Strouhal frequency (Stz) at the higher TR case exhibits a decreasing trend with remarkably smaller finite jumps at the cell boundaries and is found close to uniform cylinder flow. The wavelet analysis reveals the narrowing of the spectrum at a lower TR. A higher TR case shows a distinctly regular and evenly spaced spectrum which does not reach the maximum Stz, making it a rare event. The present results show that tapering causes the appearance of a secondary motion, which completely reverses at the downstream cylinder wake. Our numerical calculations show that pressure has an indirect role in the growth of the secondary instabilities, where isobars align along with the taper profile. The geometrically induced shear promotes greater mixing in the near wake, and we found that the maximum cross-stream velocity never exceeds 10% of the mean flow even with the steepest TR. The streamwise growth of the defect layer is slower for increasing TR and reaches an early saturation. Although the velocity deficit is higher at the steepest TR, it causes a delay in the momentum recovery along the streamwise direction. The shape factor for the lower TR case shows a delay in the laminar–turbulent transition. Finally, our global stability analysis results employing dynamic mode decomposition revealed a nonlinear dynamical system with spanwise dissipation of the dynamic modes.

中文翻译：

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大锥度比锥形圆柱体背后的三维尾流动力学

我们已经对通过锥形圆柱体的流动进行了直接数值模拟，在早期过渡到三个维度的过程中，两个连续的锥度比 (TR) 分别为 20 和 12.5。我们的结果表明涡旋分裂和位错的随机发生是脱落特征的拓扑结构。特别是，我们观察到倾斜细胞脱落具有多个展向模式和棚结构中相反定向的倾斜细胞。与流动施加的剪切不同，涡旋形成长度对锥度比变得敏感，这消除了因较低剪切速率而注意到的斜频率波。较高 TR 情况下的局部 Strouhal 频率 (Stz) 表现出下降趋势，在单元边界处有限跳跃显着减小，并且接近均匀的圆柱流。小波分析揭示了在较低的 TR 处频谱变窄。较高的 TR 情况显示出明显规则且间隔均匀的频谱，该频谱未达到最大 Stz，使其成为罕见事件。目前的结果表明，锥形导致二次运动的出现，在下游气缸尾流处完全逆转。我们的数值计算表明，压力在二次不稳定性的增长中具有间接作用，其中等压线与锥度轮廓对齐。几何诱导的剪切促进了近尾流中更大的混合，我们发现即使在最陡峭的 TR 下，最大横流速度也不会超过平均流量的 10%。缺陷层的流向生长随着 TR 的增加而变慢并达到早期饱和。尽管在最陡的 TR 处速度赤字较高，但它会导致沿流向的动量恢复延迟。下 TR 情况的形状因子显示层流-湍流过渡的延迟。最后，我们采用动态模式分解的全局稳定性分析结果揭示了一个具有动态模式展向耗散的非线性动力系统。