On Objective and Non-objective Kinematic Flow Classification Criteria
Turbulent flows present several compact and spatially coherent regions generically known as coherent structures. The understanding of these structures is closely related to the concept of vortex, whose definition is still a subject of controversy within the scientific community. In particular, the role of objectivity in the definition of vortex remains a largely open question. The three most usual criteria for vortex identification (Q, \(\varDelta \) and \(\lambda _2\)) are non-objective since they all depend on the fluid’s rate-of-rotation, which is not invariant to the reference frame. In the present work, we propose an objective definition of these criteria by using the concept of relative rate-of-rotation with respect to the principal directions of the strain rate tensor. We also explore two novel naturally objective flow classification criteria. All the criteria are applied to instantaneous velocity fields obtained by DNS of both Newtonian and viscoelastic turbulent channel flows. The analysis is carried out here for four friction Reynolds numbers from 180 to 1000, emphasizing the difference between objective and non-objective and classification criteria, as well as between Newtonian and non-Newtonian flows. Moreover, we try to obtain from the results of flow classification criteria information related to the polymer drag reduction phenomenon.
KeywordsBuffer Layer Direct Numerical Simulation Drag Reduction Anisotropic Ratio Strain Rate Tensor
This work was granted access to the HPC resources of IDRIS under the allocation 2014-i20142b2277 made by GENCI. The authors would also like to express their acknowledgment and gratitude to the Brazilian Scholarship Program Science Without Borders, managed by CNPq (National Council for Scientific and Technological Development), for the partial financial support for this research.
- 5.R. Drouot, Définition d’un transport associé à un modèle de fluide de deuxième ordre. Comparaison de diverses lois de comportement. C. R. Acad. Sci. A Math. 282, 923–926 (1976)Google Scholar
- 6.R. Drouot, M. Lucius, Approximation du second ordre de la loi de comportement des fluides simples. Lois classiques deduites de l’introduction d’un nouveau tenseur objectif. Arch. Mech. 28(2), 189–198 (1976)Google Scholar
- 7.F.C. Frank, M.R. Mackley, Localized flow birefringence of polyethylene oxide solutions in a two roll mill. J. Polym. Sci. 14, 69–76 (1976)Google Scholar
- 9.R. Huilgol, Comments on “Objective and generally applicable criteria for flow classification”, by G. Astarita. J. Non-Newton. Fluid 7(1), 91–95 (1980)Google Scholar
- 10.J.C.R. Hunt, A.A. Wray, P. Moin, Eddies, stream, and convergence zones in turbulent flows, in Proceedings of Summer Program. Center for Turbulence Research. Report CTR-S88 (1988), pp. 193–208Google Scholar