Turbulence generation in the transitional flow in the wake behind a sphere is studied with numerical simulations. The filtered Navier–Stokes equation and the large eddy simulation method are employed as the governing equation and the numerical method, respectively. The ΩR̃ vortex identification method is used to trace the evolution of vortices in the wake flow. The energy gradient theory is used to analyze the spike formation in the wake flow. The simulation results show that the vortex structure in the wake flow is the type of hairpin vortices, which is similar to that in a boundary layer flow. Ejection and sweep motions exist around the hairpin vortices. There are two most unstable regions in the wake where turbulence “burst” is first produced, one is near the center of the vortex head and the other is between the two vortex legs. There is a high-pressure zone above the vortex head due to the decrease in the streamwise velocity, and a soliton-like coherent structure exists in this area. The mechanism of turbulence generation in the wake is the discontinuity of the streamwise velocity, which makes the Navier–Stokes equation be singular. This singularity leads to the formation of the “negative spike” in the streamwise velocity. The amplitude of the “negative spike” reaches up to 60% of the incoming velocity, which is close to the situation in a boundary layer flow on a flat plate. It is concluded that the mechanism of turbulence generation in the wake flow is the same as that in the boundary layer flow.

中文翻译：

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球体后面过渡尾流中的湍流产生

通过数值模拟研究了球体后面尾流中过渡流中湍流的产生。控制方程采用滤波纳维-斯托克斯方程，数值方法采用大涡模拟法。 ΩR̃涡识别方法用于追踪尾流中涡的演化。能量梯度理论用于分析尾流中尖峰的形成。模拟结果表明，尾流中的涡结构为发夹涡类型，与边界层流中的涡结构类似。发夹涡周围存在喷射运动和扫掠运动。尾流中有两个最不稳定的区域，首先产生湍流“爆发”，一个位于涡头中心附近，另一个位于两个涡腿之间。由于流向速度降低，涡头上方存在一个高压区，该区域存在类孤子相干结构。尾流中湍流产生的机制是流向速度的不连续性，这使得纳维-斯托克斯方程具有奇异性。这种奇点导致流向速度中“负尖峰”的形成。 “负尖峰”的幅度高达来流速度的60%，接近平板上边界层流的情况。结果表明，尾流中湍流产生的机理与边界层流中湍流产生的机理相同。