Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence
Multiscale analysis of the invariants of the velocity gradient tensor in isotropic turbulence
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DOI：
10.1103/physrevfluids.3.044604
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发表时间：
2018-04-11
影响因子：
2.7
通讯作者：
Meneveau, Charles
中科院分区：
文献类型：
--
作者：
Danish, Mohammad;Meneveau, Charles
局部流动拓扑的知识，即由速度梯度张量描述的移动流体元素周围的流线模式，对于深入了解湍流过程（例如能量级联、材料元素变形或标量混合）非常有用。最近，人们对最小（粘性）湍流尺度下的流动拓扑学有了很多了解。然而，在更大的尺度上，例如在湍流的惯性尺度上，人们知之甚少。在这项工作中，我们对各种感兴趣的量的尺度依赖性进行了详细研究，例如不同类型流拓扑的总体分数、速度梯度张量的第二和第三不变量的联合概率分布，以及涡度与应变率特征向量的几何对齐。我们对 Re-lambda = 433 的各向同性湍流模拟数据集进行分析。虽然数量在惯性范围内看起来接近尺度不变，但我们在惯性范围和粘性范围之间的长度尺度上观察到多个数量的“凹凸”。例如，当减小惯性范围进入粘性范围时，不稳定节点-鞍-鞍流拓扑的总体分数显示出增加。对于涡度-应变率对齐，观察到类似的凸起。为了记录粘性和惯性范围内不同趋势的可能动力学原因，我们检查了控制速度梯度不变量的 Fokker-Plank 方程中出现的概率通量。具体来说，我们的目标是了解粘性和惯性范围统计数据之间观察到的差异是否是由于压力、亚网格尺度或粘性应力或这些术语的各种组合引起的影响。为了将流分解为小尺度和大尺度，我们主要使用具有良好空间定位特性的光谱紧凑非负滤波器（Eyink-Aluie 滤波器）。分析表明，当从惯性范围进入粘性范围时，亚网格应力效应作为尺度函数的下降速度快于粘性效应的增加速度。为了弥补这一差异，压力 Hessian 在粘性范围内的表现也与惯性范围内有所不同。结果对速度梯度张量模型有影响，表明如果希望重现观察到的趋势，则亚网格尺度的影响可能不能通过惯性范围内的恒定涡粘性简单地建模。
Knowledge of local flow-topology, the patterns of streamlines around a moving fluid element as described by the velocity-gradient tensor, is useful for developing insights into turbulence processes, such as energy cascade, material element deformation, or scalar mixing. Much has been learned in the recent past about flow topology at the smallest (viscous) scales of turbulence. However, less is known at larger scales, for instance, at the inertial scales of turbulence. In this work, we present a detailed study on the scale dependence of various quantities of interest, such as the population fraction of different types of flow-topologies, the joint probability distribution of the second and third invariants of the velocity gradient tensor, and the geometrical alignment of vorticity with strain-rate eigenvectors. We perform the analysis on a simulation dataset of isotropic turbulence at Re-lambda = 433. While quantities appear close to scale invariant in the inertial range, we observe a "bump" in several quantities at length scales between the inertial and viscous ranges. For instance, the population fraction of unstable node-saddle-saddle flow topology shows an increase when reducing the scale from the inertial entering the viscous range. A similar bump is observed for the vorticity-strain-rate alignment. In order to document possible dynamical causes for the different trends in the viscous and inertial ranges, we examine the probability fluxes appearing in the Fokker-Plank equation governing the velocity gradient invariants. Specifically, we aim to understand whether the differences observed between the viscous and inertial range statistics are due to effects caused by pressure, subgrid-scale, or viscous stresses or various combinations of these terms. To decompose the flow into small and large scales, we mainly use a spectrally compact non-negative filter with good spatial localization properties (Eyink-Aluie filter). The analysis shows that when going from the inertial range into the viscous range, the subgrid-stress effect decreases more rapidly as a function of scale than the viscous effects increase. To make up for the difference, the pressure Hessian also behaves somewhat differently in the viscous than in the inertial range. The results have implications for models for the velocity gradient tensor showing that the effects of subgrid scales may not be simply modeled via a constant eddy viscosity in the inertial range if one wishes to reproduce the observed trends.