报告内容介绍：

A vortex is intuitively recognized as the rotational/swirling motion of the fluids. However, an unambiguous and universally-accepted definition for vortex is yet to be achieved in the field of fluid mechanics, which is probably one of the major obstacles causing considerable confusions and misunderstandings in turbulence research. A new vector quantity which is called Rortex is proposed as a mathematical definition of vortex vector to accurately describe the local fluid rotation and clearly display vortical structures. The classic definition of vortex is associated with vorticity which possesses a clear mathematic definition, namely the curl of velocity vector. Helmholtz first considers a vorticity tube with infinitesimal cross-section as a vortex filament, which is followed by Lamb to simply call a vortex filament as a vortex in his classic monograph. Most of the currently popular Eulerian vortex identification criteria, including Q criterion, ∆ criterion and λ_ci criterion, are based on the local analysis of the velocity gradient tensor. More specifically, these criteria are exclusively determined by the eigenvalues of the velocity gradient tensor and thereby can be regarded as eigenvalue-based criteria. However, these criteria have been found to be plagued with two shortcomings: (1) these criteria seldom identify the swirl axis or orientation; (2) these criteria can be seriously contaminated by shearing. In this paper, an eigenvector-based interpretation of Rortex is introduced as a mathematical definition: the real eigenvector of the velocity gradient tensor is served as the possible axis of the local fluid rotation to determine the direction of Rortex, and the rotational strength obtained in the plane perpendicular to the possible axis is defined as the magnitude of Rortex. This new mathematical definition dramatically improves the computational efficiency, and more importantly, provides a novel decomposition of the velocity gradient tensor to shed light on the relations between Rortex and eigenvalue-based criteria. By relying on the decomposition, it can be clearly observed that shearing always manifests its effect on the imaginary part of complex conjugated eigenvalues and in turn contaminates eigenvalue-based criteria, while Rortex eliminates this contamination and thus can reasonably present the local rotational strength. In addition, new vorticity tensor and vector decompositions are introduced: the vorticity tensor is decomposed to a rigidly rotational part and a non-rotationally anti-symmetric part, and the vorticity vector is decomposed to a rigidly rotational vector which is called the Rortex vector and a non-rotational vector which is called the shear vector. Several cases, including 2D Couette flow, 2D rigid rotational flow and 3D boundary layer transition on a flat plate, are studied to demonstrate the justification of the definition of Rortex and to confirm the superiority of Rortex.