湍流管流中单涡对流向速度方差的贡献。第一部分：单涡强度函数

中文摘要 AI 辅助

Townsend的附着涡假设通过自相似附着涡的叠加解释了壁湍流的渐近统计特性。在给定的观测位置，活跃部分对动量传递有贡献，而非活跃部分仅保留壁平行方向的脉动。由于这一区别取决于观测高度相对于涡高度$y_l$的位置，我们从$Re_\tau\simeq930$--$6000$的湍流管流直接数值模拟（DNS）中提取单涡强度函数。谱线性随机估计和差分方法在指定的$y_l$处隔离出壁相干贡献，得到流向和壁法向强度函数$I_{uu}$和$I_{vv}$。当用$y^*=y/y_l$表示时，两者在不同$y_l$下均发生重合，并在接近von Kármán常数的$y_a^*$处共享一个峰值。在$y_a^*$附近，两个分量均保持显著，而对于$y^*\ll y_a^*$，$I_{vv}$减小而$I_{uu}$保持有限，从而识别出活跃和非活跃部分。在自相似范围内，两个峰值强度均按$y_l^{-1}$缩放，且$I_{uu}$在两个部分均保持此缩放。对活跃部分积分得到近似恒定的贡献，而非活跃部分恢复了经典的近壁对数变化。对活跃部分积分至其外截止，产生了斜率接近Townsend--Perry常数的外对数趋势。在$\langle uu\rangle^+$的近壁峰值处，缩放关系陡化为$I_{uu}\sim y_l^{-(1+\beta)}$，其中$\beta\simeq1/4$，产生具有$Re_\tau^{-1/4}$缺陷的有限渐近线。额外的指数归因于与$y_l$相关的耗散尺度对非活跃足迹的粘性衰减。壁相干运动还产生宽的外肩，而局部壁不相干残差可能对次级峰值有贡献。

英文摘要

Townsend's attached-eddy hypothesis explains the asymptotic statistics of wall turbulence through a superposition of self-similar attached eddies. At a given observation location, active portions contribute to momentum transfer, whereas inactive portions retain only wall-parallel fluctuations. Since this distinction depends on the observation height relative to the eddy height $y_l$, we extract single-eddy intensity functions from DNS of turbulent pipe flow at $Re_τ\simeq930$--$6000$. Spectral linear stochastic estimation and differencing isolate wall-coherent contributions at prescribed $y_l$, yielding the streamwise and wall-normal intensity functions $I_{uu}$ and $I_{vv}$. When expressed in $y^*=y/y_l$, both collapse across $y_l$ and share a peak at $y_a^*$, close to the von K'arm'an constant. Near $y_a^*$, both components remain significant, whereas for $y^*\ll y_a^*$, $I_{vv}$ diminishes while $I_{uu}$ remains finite, identifying active and inactive portions. Over the self-similar range, both peak intensities scale as $y_l^{-1}$, and $I_{uu}$ retains this scaling in both portions. Integrating the active portion yields an approximately constant contribution, while the inactive portion recovers the classical near-wall logarithmic variation. An outer logarithmic tendency with a slope close to the Townsend--Perry constant arises from integrating active contributions up to their outer cutoff. At the near-wall peak of $\langle uu\rangle^+$, the scaling steepens to $I_{uu}\sim y_l^{-(1+β)}$ with $β\simeq1/4$, yielding a finite asymptote with a $Re_τ^{-1/4}$ defect. The additional exponent is attributed to viscous attenuation of inactive footprints associated with a $y_l$-dependent dissipative scale. Wall-coherent motions also produce a broad outer shoulder, while a localized wall-incoherent residual may contribute to a secondary peak.

发表机构

• School of Mechanical Engineering, Pusan National University（釜山国立大学机械工程学院）

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