标题： 低雷诺数随机流中速度梯度统计的渐近预测：偏斜度、间歇性和对齐的出现 显示英文标题

标题： Asymptotic predictions on the velocity gradient statistics in low-Reynolds number random flows: Onset of skewness, intermittency and alignments

摘要： 通过在趋于零的雷诺数下通过高斯强迫搅拌流体，会产生高斯随机场，而在较高雷诺数下的流动表现出非高斯性、级联、异常标度和优先对齐。最近的研究（Yakhot和Donzis，Phys. Rev. Lett., 第119卷，2017年，第044501页；Gotoh和Yang，Philos. Trans. Royal Soc. A, 第380卷，2022年，第20210097页）通过关注速度增量的标度来研究低雷诺数流动中这些湍流特征的出现。他们表明，在低雷诺数随机流动和高雷诺数湍流中的标度出人意料地相似。在本工作中，我们从速度梯度动力学的角度探讨低雷诺数流动中湍流特征的出现，提供了对其丰富统计几何的见解。我们将完整的纳维-斯托克斯方程的微扰理论与速度梯度建模相结合。该过程产生了一个速度梯度的随机模型，其中模型系数直接来自纳维-斯托克斯方程和统计同质性约束。与我们的随机模型相关的福克-普朗克方程具有解析解，该解显示了低雷诺数下湍流特征的出现：随着雷诺数的增加，速度梯度统计中会出现偏度、间歇性和优先对齐。模型预测与低雷诺数流动的直接数值模拟结果高度一致。 显示英文摘要

摘要： Stirring a fluid through a Gaussian forcing at a vanishingly small Reynolds number produces a Gaussian random field, while flows at higher Reynolds numbers exhibit non-Gaussianity, cascades, anomalous scaling and preferential alignments. Recent works (Yakhot and Donzis, Phys. Rev. Lett., vol. 119, 2017, pp. 044501; Gotoh and Yang, Philos. Trans. Royal Soc. A, vol. 380, 2022, pp. 20210097) investigated the onset of these turbulent hallmarks in low-Reynolds number flows by focusing on the scaling of the velocity increments. They showed that the scalings in random flows at low-Reynolds and in high-Reynolds number turbulence are surprisingly similar. In this work, we address the onset of turbulent signatures in low-Reynolds number flows from the viewpoint of the velocity gradient dynamics, giving insights into its rich statistical geometry. We combine a perturbation theory of the full Navier-Stokes equations with velocity gradient modeling. This procedure results in a stochastic model for the velocity gradient in which the model coefficients follow directly from the Navier-Stokes equations and statistical homogeneity constraints. The Fokker-Planck equation associated with our stochastic model admits an analytic solution which shows the onset of turbulent hallmarks at low Reynolds numbers: skewness, intermittency and preferential alignments arise in the velocity gradient statistics as the Reynolds number increases. The model predictions are in excellent agreement with direct numerical simulations of low-Reynolds number flows.