An elliptical region method for identifying a vortex with indications of its compressibility and swirling pattern

A local trace criterion (LT_cri) is proposed to identify the vortex, and a projection plane with an analytical elliptical region (ER) corresponding to the LT_cri is constructed to indicate the compressibility and swirling pattern of the recognised vortex region simultaneously. The analytical expression of the three components of the complex eigenvalues are provided to formulate the positive-Delta space as the projection plane. Flow points that projected inside the elliptical region could be thought as constructing the vortex with the projected location indicating the compressibility and the swirling patterns of the local fluid. With the analytical resolution given, the LT_cri based ER (LTER) indication method is easy to implement in a pointwise manner, and it is suitable for the local analysis of a time-frozen flow field, both compressible and incompressible. The method is also Galilean invariant and it overcomes the imperfection of threshold choice in region-type methods. A compressor corner separation flow case with practical Mach number is analysed by the LTER indication method. The potential of the proposed method is shown both in distinguishing the different swirling patterns of complex vortices in tangle as well as analysing their evolution mechanism, through the regional indication.