Study of the velocity gradient tensor in turbulent flow
Study of the velocity gradient tensor in turbulent flow
复制标题
湍流中速度梯度张量的研究
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
B. Cantwell
中科院分区：
文献类型：
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作者：
W. Cheng;B. Cantwell
用直接数值模拟得到的三种湍流流场研究了速度梯度张量A（ij）= Δ u（i）/Δ x（j）的行为。流场研究包括：两个涡流管之间相互作用的无粘计算、均匀各向同性流和随时间变化的平面尾迹。当用平均应变率对A（ij）进行归一化时，获得了每个流动的自相似行为。两个涡管之间的相互作用的情况下，揭示了一个有限尺寸的相干结构的拓扑特征，可预测的限制欧拉模型。当流动接近奇点时，这种结构随着峰值涡量的变化而变化。该结构中的A（ij）的不变量遵循以下形式的直线关系：gamma（sup 3）+gammaQ+R=0，其中Q和R是A（ij）的第二和第三不变量，并且本征值gamma在该结构的体积上几乎恒定。该结构中的数据具有不稳定节点/鞍/鞍的局部应变拓扑。对于均匀各向同性流和随时间变化的平面尾流，还研究了速度梯度张量和相关加速度梯度张量H（ij）的各向异性部分的特性。结果表明，H（ij）的应变率张量的中间主特征值趋于负值，局部应变拓扑为稳定节点/鞍/鞍型.也有一个优先的特征值方向。当数据在高局部耗散区域时，尾流中的H（ij）的大小被发现是非常小的。这一结果在雷诺数相对较低的均匀各向同性流的模拟中没有观察到。A（ij）的演化的一个限制性欧拉模型被发现再现了许多在模拟中确定的拓扑特征。
The behavior of the velocity gradient tensor, A(ij)=delta u(i)/delta x(j), was studied using three turbulent flows obtained from direct numerical simulation The flows studies were: an inviscid calculation of the interaction between two vortex tubes, a homogeneous isotropic flow, and a temporally evolving planar wake. Self-similar behavior for each flow was obtained when A(ij) was normalized with the mean strain rate. The case of the interaction between two vortex tubes revealed a finite sized coherent structure with topological characteristics predictable by a restricted Euler model. This structure was found to evolve with the peak vorticity as the flow approached singularity. Invariants of A(ij) within this structure followed a straight line relationship of the form: gamma(sup 3)+gammaQ+R=0, where Q and R are the second and third invariants of A(ij), and the eigenvalue gamma is nearly constant over the volume of this structure. Data within this structure have local strain topology of unstable-node/saddle/saddle. The characteristics of the velocity gradient tensor and the anisotropic part of a related acceleration gradient tensor H(ij) were also studied for a homogeneous isotropic flow and a temporally evolving planar wake. It was found that the intermediate principal eigenvalue of the rate-of-strain tensor of H(ij) tended to be negative, with local strain topology of the type stable-node/saddle/saddle. There was also a preferential eigenvalue direction. The magnitude of H(ij) in the wake flow was found to be very small when data were conditioned at high local dissipation regions. This result was not observed in the relatively low Reynolds number simulation of homogeneous isotropic flow. A restricted Euler model of the evolution of A(ij) was found to reproduce many of the topological features identified in the simulations.