On the evolution of material lines and vorticity in homogeneous turbulence

Michele Guala, Beat Lüthi, Alexander Liberzon, Arkady Tsinober, Wolfgang Kinzelbach

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46 Scopus citations

Abstract

The evolution of material lines, l, and vorticity, ω, is investigited experimentally through three-dimensional particle-tracking velocimetry (3D-PTV) in quasi-homogeneous isotropic turbulence at Reλ. = 50. Through 3D-PTV data the full set of velocity derivatives, ∂ui/∂xj, is accessible. This allows us to monitor the evolution of various turbulent quantities along fluid particle trajectories. The main emphasis of the present work is on the physical mechanisms that govern the Lagrangian evolution of l ω and the essential differences inherent in these two processes. For example, we show that vortex stretching is smaller than material lines stretching, i.e. 〈ωiωj sij2〉 < 〈li ljsij/l2〉, and expand on how this issue is closely related to the predominant alignment of ω and the intermediate principal strain eigenvector λ2 of the rate of strain tensor, Sij, By focusing on Lagrangian quantities we discern whether these alignments are driven and maintained mainly by vorticity or by strain. In this context, the tilting of ω and the rotation of the eigenframe λi of the rate of strain tensor Sij are investigated systematically conditioned on different magnitudes of strain, s2, and enstrophy, ω2 Further, we infer that viscosity contributes through the term vωi2ωi to Dω2/Dt, whereas Dl2/Dt has no diffusive term. This difference plays a key role in defining the mutual orientation between ω and λi. Viscosity thus contributes significantly to the difference in growth rates of 〈ωiωjsij〉 and 〈liljsij〉.

Original languageEnglish (US)
Pages (from-to)339-359
Number of pages21
JournalJournal of Fluid Mechanics
Volume533
DOIs
StatePublished - Jun 25 2005

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