Abstract
The third-generation vortex identification method of Liutex (previously called Rortex) was introduced by the team led by Prof. Chaoqun Liu from University of Texas at Arlington to mathematically extract the rigid rotation part from the fluid motion, and thus to define and visualize vortices. Unlike the vorticity-based first generation and the scalar-valued second generation, Q, λ2, Δ and λci methods for example, the Liutex vector provides a unique, mathematical and systematic way to define vortices and visualize vortical structures from multiple perspectives without ambiguity. In this article, we summarize the recent developments of the Liutex framework and discuss the Liutex theoretical system including its existence, uniqueness, stability, Galilean invariance, locality and globality, decomposition in tensor and vector forms, Liutex similarity in turbulence, and multiple Liutex-based vortex visualization methods including Liutex lines, Liutex magnitude iso-surfaces, Liutex-Ω method, and Liutex core line method, etc.. Thereafter, the six core elements of vortex identification, including (1) absolute strength, (2) relative strength, (3) local rotational axis, (4) vortex rotation axes, (5) vortex core size, (6) vortex boundary, are used as touchstones against which the Liutex vortex identification system is examined. It is demonstrated with illustrative examples that the Liutex system is able to give complete and precise information of all six core elements in contrast to the failure and inaccuracy of the first and second-generation methods. The important concept that vorticity cannot represent vortex and the superiority of the Liutex system over previous methods are reiterated and stated in appropriate places throughout the paper. Finally, the article concludes with future perspectives, especially the application of the Liutex system in studying turbulence mechanisms encouraged by the discovery of Liutex similarity law. As a newly defined physical quantity, Liutex may open a door for quantified vortex and turbulence research including Liutex (vortex) dynamics and lead the community out of the shadow of turbulence research which traditionally relies on observations, graphics, assumptions, hypotheses, and other qualitative analyses. An optimistic projection is that the Liutex system could be critical to investigation of the vortex dynamics in applications from hydrodynamics, aerodynamics, oceanography, meteorology, etc. and to research of the generation, sustenance, modelling and controlling of turbulence.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Liu C., Gao Y. S., Dong X. R. et al. Third generation of vortex identification methods: Omega and Liutex/Rortex based systems [J]. Journal of Hydrodynamics, 2019, 31(2): 205–223.
Robinson S. K. Coherent motion in the turbulent boundary layer [J]. Annual Review of Fluid Mechanics, 1991, 23: 601–639.
Wang Y., Yang Y., Yang G. et al. DNS study on vortex and vorticity in late boundary layer transition [J]. Communications in Computational Physics, 2017, 22(2): 441–459.
Hunt J., Wray A., Moin P. Eddies, streams, and convergence zones in turbulent flows [R]. Proceedings of the Summer Program. Center for Turbulence Research Report CTR-S88, 1988, 193–208.
Jeong J., Hussain F. On the identification of a vortex [J]. Journal of Fluid Mechanics, 1995, 285: 69–94.
Chong M., Perry A., Cantwell B. A general classification of three-dimensional flow fields [J]. Physics of Fluids A, 1990, 2: 765–777.
Zhou J., Adrian R., Balachandar S. et al. Mechanisms for generating coherent packets of hairpin vortices in channel flow [J]. Journal of Fluid Mechanics, 1999, 387: 252–296.
Liu C., Yan Y., Lu P. Physics of turbulence generation and sustenance in a boundary layer [J]. Computers and Fluids, 2014, 102: 353–384.
Liu C., Wang Y. Q., Yang Y. et al. New Omega vortex identification method [J]. Science China: Physics, Mechanics and Astronomy, 2016, 59(8): 684711.
Gui N., Ge L., Cheng P. X. et al. Comparative assessment and analysis of rorticity by Rortex in swirling jets [J]. Journal of Hydrodynamics, 2019, 31(3): 495–503.
Wang L., Zheng Z., Cai W. H. et al. Extension of Omega and Omega-Liutex methods to the identification of vortex structures in viscoelastic turbulent flow [J]. Journal of Hydrodynamics, 2019, 31(5): 911–921.
Wang Y. F., Zhang W. H., Cao X. et al. A discussion on the applicability of vortex identification methods for complex vortex structures in axial turbine rotor passages [J]. Journal of Hydrodynamics, 2019, 31(4): 700–707.
Wang C. C., Liu Y., Chen J. et al. Cavitation vortex dynamics of unsteady sheet/cloud cavitating flows with shock wave using different vortex identification methods [J]. Journal of Hydrodynamics, 2019, 31(3): 475–494.
Zhang Y. N., Liu K. H., Li J. W. et al. Analysis of the vortices in the inner flow of reversible pump turbine with the new omega vortex identification method [J]. Journal of Hydrodynamics, 2018, 30(3): 463–469.
Liu C., Gao Y., Tian S., Dong X. Rortex-A new vortex vector definition and vorticity tensor and vector decompositions [J]. Physics of Fluids, 2018, 30(3): 034103.
Gao Y., Liu C. Rortex and comparison with eigenvalue-based vortex identification criteria [J]. Physics of Fluids, 2018, 30(8): 085107.
Wang Y. Q., Gao Y. S., Liu J. M. et al. Explicit formula for the Liutex vector and physical meaning of vorticity based on the Liutex-Shear decomposition [J]. Journal of Hydrodynamics, 2019, 31(3): 464–474.
Dong X., Gao Y., Liu C. New normalized Rortex/vortex identification method [J]. Physics of Fluids, 2019, 31(1): 011701.
Liu J., Liu C. Modified normalized Rortex/vortex identification method [J]. Physics of Fluids, 2019, 31(6): 061704.
Gao Y. S., Liu J. M., Yu Y. F. et al. A Liutex based definition of vortex rotation axis line [J]. Journal of Hydrodynamics, 2019, 31(3): 445–454.
Xu H., Cai X. S., Liu C. Liutex (vortex) core definition and automatic identification for turbulence vortex structures [J]. Journal of Hydrodynamics, 2019, 31(5): 857–863.
Liu J., Gao Y., Liu C. An objective version of the Rortex vector for vortex identification [J]. Physics of Fluids, 2019, 31(6): 065112.
Liu J. M., Gao Y. S., Wang Y. Q. et al. Objective Omega vortex identification method [J]. Journal of Hydrodynamics, 2019, 31(3): 455–463.
Xu W. Q., Wang Y. Q., Gao Y. S. et al. Liutex similarity in turbulent boundary layer [J]. Journal of Hydrodynamics, 2019, 31(6): 1259–1262.
Wang Y. Q., Gui N. A review of the third-generation vortex identification method and its applications [J]. Chinese Journal of Hydrodynamics, 2019, 34(4): 413–429(in Chinese).
Wang Y., Gao Y., Liu C. Letter: Galilean invariance of Rortex [J]. Physics of Fluids, 2018, 30(11): 111701.
Dong X. R., Wang Y. Q., Chen X. P. et al. Determination of epsilon for Omega vortex identification method [J]. Journal of Hydrodynamics, 2018, 30(4): 541–548.
Acknowledgments
This work was mainly supported by the Department of Mathematics of University of Texas at Arlington where the corresponding author, Dr. Chaoqun Liu, is the full-time professor. The authors are grateful to Texas Advanced Computational Center (TACC) for providing computation hours. This work is accomplished by using code DNSUTA developed by Dr. Chaoqun Liu at the University of Texas at Arlington.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, Yq., Gao, Ys., Xu, H. et al. Liutex theoretical system and six core elements of vortex identification. J Hydrodyn 32, 197–211 (2020). https://doi.org/10.1007/s42241-020-0018-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42241-020-0018-0