聚合物湍流衰减的物理机制：时间尺度视角
Physical mechanism of turbulence attenuation by polymers from a timescale perspective
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中文总结 AI 辅助
本研究通过直接数值模拟和尺度分解，提出尺度依赖的魏森贝格数，揭示聚合物从较小尺度到较大尺度逐步抑制涡旋的机制，并建立了聚合物-湍流相互作用的物理图像。
中文摘要 AI 辅助
为阐明聚合物在各尺度上衰减湍流的物理机制，我们对稀聚合物溶液中的均匀各向同性湍流进行了直接数值模拟。我们将聚合物建模为FENE哑铃，并使用布朗动力学进行模拟。通过可视化相干涡旋的层级结构，我们证明随着魏森贝格数增加，聚合物从较小尺度到较大尺度逐步抑制涡旋，从而衰减其湍动能。受Lumley理论启发，我们提出了一种基于时间尺度的新框架，利用尺度分解来分析这一衰减过程。我们定义了一个尺度依赖的魏森贝格数$\mathrm{Wi}_{\mathrm{sd}}(k)$，即聚合物松弛时间与各波数下多尺度涡旋周转时间之比。我们揭示，当以$\mathrm{Wi}_{\mathrm{sd}}(k)$表示时，各尺度的能量衰减率汇聚到一条单一曲线上，该曲线在$\mathrm{Wi}_{\mathrm{sd}}(k) \gtrsim 1$处上升，证明$\mathrm{Wi}_{\mathrm{sd}}(k)$成功描述了任意给定尺度$k^{-1}$下湍流衰减的起始和程度。此外，尺度分解揭示，聚合物在满足$\mathrm{Wi}_{\mathrm{sd}}(k) \approx 1$的尺度上优先与湍流拉伸方向对齐。基于这些结果，我们建立了聚合物-湍流相互作用的物理图像，并将其明确与聚合物衰减湍流中的统计量联系起来。
英文摘要
To elucidate the physical mechanism of turbulence attenuation by polymers at each scale, we conduct direct numerical simulations of homogeneous isotropic turbulence in dilute polymer solutions. We model polymers as FENE dumbbells and simulate them using Brownian dynamics. By visualising the hierarchical structures of coherent vortices, we demonstrate that as the Weissenberg number increases, polymers progressively suppress vortices from smaller to larger scales, attenuating their turbulent energy. While inspired by Lumley's theory, we propose a novel timescale-based framework for analysing this attenuation process using the scale decomposition. We define a scale-dependent Weissenberg number, $\mathrm{Wi}_{\mathrm{sd}}(k)$, as the ratio of the polymer relaxation time to the turnover time of multiscale vortices at each wave-number. We reveal that when expressed in terms of $\mathrm{Wi}_{\mathrm{sd}}(k)$, the energy attenuation rate at each scale collapses onto a single curve that rises at $\mathrm{Wi}_{\mathrm{sd}}(k) \gtrsim 1$, proving that $\mathrm{Wi}_{\mathrm{sd}}(k)$ successfully describes both the onset and the degree of turbulence attenuation at any given scale $k^{-1}$. Furthermore, the scale decomposition uncovers that polymers preferentially align with the turbulent stretching direction at the scale satisfying $\mathrm{Wi}_{\mathrm{sd}}(k) \approx 1$. Based on these results, we establish a physical picture of the polymer--turbulence interaction and explicitly link it to the statistics in turbulence attenuated by polymers.
