非均匀湍流中间歇性与耗散关系的综合分析

中文摘要 AI 辅助

近期对多种湍流的研究表明，间歇性和耗散在均匀各向同性湍流（HIT）之外也表现出一致的标度行为。对于湍流尾流、格栅湍流和湍流射流，耗散参数$C_\varepsilon$和间歇性参数$\mu$会变化，而它们的乘积保持不变，与雷诺数$Re_\lambda$无关。在此，我们将这一结果从中心线热线测量扩展到非中心线数据，包括具有显著剪切的区域。我们确定了两个额外关系：$(\gamma-1)C_\varepsilon$保持不变，其中$\gamma$是惯性区绝对谱斜率，且$\gamma$与科尔莫戈罗夫参数$C_k$线性变化。主要约束是大尺度增量概率密度函数为高斯分布，表明大尺度随机驱动。这些关系将变化的量$C_\varepsilon$、$\mu$、$\gamma$和$C_k$简化为三个常数，并定义了一种湍流状态，该状态可由这些参数中的任何一个表征，与剪切、流动类型或雷诺数无关。我们进一步表明，对于给定的流动配置，$C_\varepsilon$依赖于$Re_\lambda$和湍流强度$TI$。由于这四个参数在名义HIT值周围广泛变化，我们将此框架解释为HIT向非均匀湍流的推广。广泛的鲁棒性测试表明，结果对具体的后处理方法不敏感。我们还分析了它们的流向和空间演化，并表明测得的$C_\varepsilon$可用于在量化不确定性内预测$\mu$、$\gamma$和$C_k$。因此，该框架连接了湍流的关键前导阶特征，同时恢复了既定的HIT趋势。

英文摘要

A recent study of various turbulent flows showed that intermittency and dissipation exhibit consistent scaling behavior beyond homogeneous isotropic turbulence (HIT). For turbulent wakes, grid turbulence, and a turbulent jet, the dissipation parameter $C_\varepsilon$ and intermittency parameter $μ$ vary while their product remains constant, independently of the Reynolds number $Re_λ$. Here, we extend this result from centerline hot-wire measurements to non-centerline data, including regions with significant shear. We identify two additional relations: $(γ-1)C_\varepsilon$ remains constant, where $γ$ is the absolute inertial-range spectral slope, and $γ$ varies linearly with the Kolmogorov parameter $C_k$. The main constraint is that the large-scale increment probability density function is Gaussian, indicating random large-scale driving. These relations reduce the varying quantities $C_\varepsilon$, $μ$, $γ$, and $C_k$ to three constants and define a turbulence state that can be characterized by any one of these parameters, independently of shear, flow type, or Reynolds number. We further show that, for a given flow configuration, $C_\varepsilon$ depends on $Re_λ$ and turbulence intensity $TI$. Because the four parameters vary over broad ranges around their nominal HIT values, we interpret this framework as a generalization of HIT to inhomogeneous turbulence. Extensive robustness tests show that the results are insensitive to the specific post-processing method. We also analyze their streamwise and spatial evolution and show that a measured $C_\varepsilon$ can be used to predict $μ$, $γ$, and $C_k$ within quantified uncertainty. The framework thus links key leading-order features of turbulence while recovering established HIT trends.

发表机构

• Univ. Grenoble Alpes, CNRS, Grenoble INP, LEGI（格勒诺布尔阿尔卑斯大学）
• Institut für Physik und ForWind, Universität Oldenburg（奥尔登堡大学）
• Univ. Lille, CNRS, ONERA, Arts et Métiers ParisTech, Centrale Lille, FRE 2017 - LMFL - Laboratoire de Mécanique des fluides de Lille - Kampé de Feriet（里尔大学）
• Institut universitaire de France (IUF)（法国高等研究院）

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