On the effectiveness of local vortex identification criteria in the compressed representation of wall-bounded turbulence

Abstract: Compressing complex flows into a tangle of vortex filaments is the basic implication of the classical notion of the vortex representation. Various vortex identification criteria have been proposed to extract the vortex filaments from available velocity fields, which is an essential procedure in the practice of the vortex representation. This work focuses on the effectiveness of those identification criteria in the compressed representation of wall-bounded turbulence. Five local identification criteria regarding the vortex strength and three criteria for the vortex axis are considered. To facilitate the comparisons, this work first non-dimensionalize the criteria of the vortex strength based on their dimensions and root mean squares, with corresponding equivalent thresholds prescribed. The optimal definition for the vortex vector is discussed by trialling all the possible combinations of the identification criteria for the vortex strength and the vortex axis. The effectiveness of those criteria in the compressed representation is evaluated based on two principles: (1) efficient compression, which implies the less information required, the better for the representation; (2) accurate decompression, which stresses that the original velocity fields could be reconstructed based on the vortex representation in high accuracy. In practice, the alignment of the identified vortex axis and vortex isosurface, and the accuracy for decompressed velocity fields based on those criteria are quantitatively compared. The alignment degree is described by using the differential geometry method, and the decompressing process is implemented via the two-dimensional field-based linear stochastic estimation. The results of this work provide some reference for the applications of vortex identification criteria in wall-bounded turbulence.