AI 中文总结
研究圆盘后高雷诺数尾流多尺度动力学，通过多种统计量分析及分解方法，揭示湍动能平衡、尺度间通量等特性，表明瞬时级联 - 耗散不平衡是湍流固有，大尺度非定常等因素使其显现。
AI 中文摘要
湍流钝体尾流体现了大尺度相干结构和小尺度湍流的共存，这两个尺度通过湍流级联相连。本文研究了圆盘后高雷诺数尾流中的多尺度动力学。首先考察了单点和两点统计量，包括湍动能（TKE）的收支和谱。发现流向平流对TKE平衡贡献最大，而耗散率不遵循经典平衡标度（$\varepsilon \nsim \mathcal{U}^3/\mathcal{L}$）。最大尺度由谱正交分解提取的三维相干模态表示，而TKE和雷诺剪切应力谱呈现惯性区标度。基于滤波的三重分解进一步将波动分离为大尺度和小尺度分量，并对动能进行划分，每个尺度有各自的空间输运以及尺度间的传递。尺度间通量表明存在统计上的正向级联并遵循经典的$\mathcal{U}^3/\mathcal{L}$标度，其径向分布变得自相似。尺度间通量与耗散之间的不平衡源于亚滤波尺度上不可忽略的流向平流。最后，耗散系数与局部泰勒雷诺数之间的反相关关系$C_\varepsilon = \varepsilon \mathcal{L}/\mathcal{U}^3 \sim Re_\lambda^{-1}$，源于粗粒化、局部平均统计量中的类似相关性。结果表明，瞬时级联 - 耗散不平衡是湍流固有的，当大尺度非定常性和长度尺度增长阻止统计平衡时变得明显。
英文摘要
Turbulent bluff-body wakes exemplify the coexistence of large-scale coherent structures and fine-scale turbulence -- two ends of a wide dynamical range of scales connected through the turbulent cascade. In this work, we study the multiscale dynamics in the high-Reynolds-number wake behind a circular disk. One-point and two-point statistics are first examined, including the budget and spectra of the turbulent kinetic energy (TKE). Streamwise advection is found to contribute the most to the TKE balance, while the dissipation rate does not follow the classical equilibrium scaling ($\varepsilon \nsim \mathcal{U}^3/\mathcal{L}$). The largest scales are represented by the three-dimensional coherent modes extracted using spectral proper orthogonal decomposition, whereas the TKE and Reynolds shear stress spectra exhibit inertial-range scalings. A filtering-based triple decomposition further separates the fluctuations into large- and small-scale components and partitions the kinetic energy, with respective spatial transports at each scale and an inter-scale transfer in between. The inter-scale fluxes indicate a statistical forward cascade and follow the classical $\mathcal{U}^3/\mathcal{L}$ scaling, while their radial profiles become self-similar. The disequilibrium between inter-scale flux and dissipation is shown to arise from non-negligible streamwise advection at the sub-filter scale. Finally, the observed anti-correlation between the dissipation coefficient and the local Taylor Reynolds number, $C_\varepsilon = \varepsilon \mathcal{L}/\mathcal{U}^3 \sim Re_λ^{-1}$, is shown to originate from a similar correlation in the coarse-grained, locally averaged statistics. The results suggest that the instantaneous cascade-dissipation disequilibrium is intrinsic to turbulence and becomes apparent when large-scale unsteadiness and length-scale growth prevent statistical equilibrium.
