We investigate energy transfer mechanisms for vortex shedding in the two-dimensional cylinder wake at a Reynolds number of $\text{Re}=100$. In particular, we focus on a comparison of the energy transfer in the true flow field to that predicted by resolvent analysis. The energy balances achieved by the true cylinder flow are first characterized—both for the flow as a whole and for each of its most energetic harmonic frequencies. It is found that viscous dissipation balances production when each is considered over the entire flow field and therefore that linear mechanisms achieve an energy balance on their own, thus respecting the Reynolds–Orr equation. Suitable energy conservation laws reveal that while nonlinear mechanisms neither produce nor consume energy overall, they nevertheless account for an important transfer of energy to higher frequencies. The energy balance for DNS is compared to that predicted by resolvent analysis. Although a suitable energy balance is achieved for each harmonic, resolvent analysis does not correctly model nonlinear energy transfer between temporal frequencies since it only models interactions between the mean flow and fluctuations. The impact of the neglected nonlinear energy transfer on the resolvent mode shapes is also made clear by analyzing the spatial distribution of the energy transfer mechanisms. We then investigate the detailed roles of energy transfer from the viewpoint of nonlinear triadic interactions by considering a finite number of harmonic frequencies. It is shown that interfluctuation interactions play a critical role in the redistribution of energy to higher harmonic frequencies. We observe not only an energy cascade from low frequencies to high frequencies, but also a considerable inverse cascade from high frequencies to low frequencies. The true energy pathways observed among harmonic modes provide additional constraints that could help to improve the modeling of nonlinear energy transfer in the cylinder flow.

中文翻译：

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圆柱尾流中的能量传递机理和解析度分析

我们研究了在雷诺数为2的二维圆柱尾流中涡流脱落的能量转移机制。 $\text{回覆}=100$。特别是，我们着重于将真实流场中的能量传递与解析分析所预测的能量传递进行比较。首先描述了通过真实汽缸流量实现的能量平衡-既针对流量整体，也针对其每个最高能谐波频率。我们发现，当在整个流场中考虑每个因素时，粘性耗散会平衡生产，因此，线性机构自身会实现能量平衡，因此遵守了雷诺兹-奥尔方程。合适的能量守恒定律表明，尽管非线性机制既不产生也不消耗任何能量，但是它们却占了能量向更高频率的重要传递。将DNS的能量平衡与解析分析所预测的能量平衡进行比较。尽管为每个谐波都实现了适当的能量平衡，但是分解剂分析不能正确地模拟时间频率之间的非线性能量传递，因为它仅模拟了平均流量和波动之间的相互作用。通过分析能量转移机制的空间分布，也可以清楚地忽略非线性能量转移对分辨模式形状的影​​响。然后，我们通过考虑有限数量的谐波频率，从非线性三重相互作用的角度研究能量转移的详细作用。结果表明，互作用相互作用在能量重新分配到高次谐波频率中起着关键作用。我们不仅观察到从低频到高频的能量级联，但是从高频到低频也有相当大的逆级联。在谐波模式之间观察到的真实能量路径提供了其他约束条件，可以帮助改善气缸流中非线性能量传递的建模。