Abstract A numerical simulation on the rise behaviour of a bubble rising in stagnant water at Re ≈ 800–1300 has been conducted. It is found that vorticity generated at the side of the bubble is transferred to the wake region, forming chains of hairpin vortices that are regularly shed and transported downstream. The resulting fluctuations in shape, trajectory, and rise velocity were found to conform well to experimental observations. The fluctuations in velocity resulting from the unsteady wakes were analysed through a fixed-frame approach about the centre of mass of the bubble. The average turbulent kinetic energy in the near wake region was found to be ≈1.4–4.8% with respect to the average kinetic energy of the bubble. The production of the turbulent kinetic energy was found to occur predominantly at the near wake region of the bubble, mostly as a result of normal and tangential gradients of the mean streamwise velocity. Interestingly, several regions of negative rate of energy production were identified, namely at the top and side interfaces of the bubble. Overall, the ratio of positive-to-negative production rate was found to be ≈2.4–3.1, resulting in a net conversion towards smaller-scale fluctuations from the mean flow. Small–scale dissipation was found to occur throughout the wake of the bubble.

中文翻译：

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水中气泡周围的能量产生和消散特征

摘要 对在 Re ≈ 800-1300 的死水中上升的气泡的上升行为进行了数值模拟。发现在气泡一侧产生的涡流被转移到尾流区域，形成有规律地脱落并向下游输送的发夹涡链。发现由此产生的形状、轨迹和上升速度的波动与实验观察结果非常吻合。通过围绕气泡质心的固定框架方法分析了由不稳定尾流引起的速度波动。发现近尾流区域的平均湍流动能约为气泡平均动能的 1.4-4.8%。发现湍流动能的产生主要发生在气泡的近尾流区域，主要是平均流向速度的法向和切向梯度的结果。有趣的是，确定了几个能量产生负率的区域，即气泡的顶部和侧面界面。总体而言，发现正负生产率之比约为 2.4-3.1，导致从平均流量向较小尺度波动的净转换。发现在气泡的整个尾流中都发生了小规模的耗散。