摘要:
本文基于速度梯度张量分析，对其中四种ω判据、Q判据、?判据、λci判据的物理意义和局限性进行分析，揭示各判据常用等值面展示的涡形态或强度的实际物理意义。首次采用基于速度梯度张量正规性的四元分解，将流体微元的运动分解为胀缩、沿正规标架的轴向变形、做平面运动和简单剪切，使得各涡判据的运动学意义更加清晰。涡量ω反映的流体微元的平均转动中总是包含简单剪切运动； Q判据可揭示流体微元在复特征向量平面上净转动相对于轴向变形的强弱，是净转动存在的充分但非必要条件；?判据能准确辨别净转动是否存在，却无法表示出净转动的强度；在净转动存在的前提下，λci可反映其绝对强度大小，净转动是复特征向量平面内正规转动和简单剪切的总和效果，正规转动是最基本的转动。新引入的四元分解方法有利于深入了解流体的涡及其运动。
Abstract:
Vortices play a crucial role in fluid dynamics, which is closely related to fluid diffusion mixing, force, heat, and noise. Five widely-used vortex identification criteria, i.e. theω-criterion, Q-criterion,?-criterion,λci-criterion, andλ2-criterion are analyzed, and four of them are compared with each other based on the velocity-gradient-tensor decomposition method. A new quadruple decomposition method (QDM) is introduced for the first time, so far as we know, to decompose fluid motions into four fundamental components: dilatation, axial deformation along the principal axes of the strain-range sensor, planar motion, and pure shearing. This method helps make the kinematic implications of the four vortex identification criteria more clear. It is found that the mean rotation of fluid elements always contains the pure shearing motion. Non-zero mean rotation ω does not guarantee the existence of the spiraling streamlines, e.g. in a typically parallel shear flow. A positive Q value indicates the strength of the pure rotation of a fluid element in the 2D complex eigenvalue plane on top of the axial deformation, which however is a sufficient but not a necessary condition for the existence of pure rotation. The ?-criterion can correctly tell the existence of pure rotation, but cannot accurately determine its strength. Theλci-value represents the absolute strength of the pure rotation, which is the combined effect of the canonical rotation in the complex eigenvector plane and the pure shearing. The proposed QDM enables us to achieve a deeper understanding of vortices and motions in fluid dynamics.
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