The evolution of small-scale structures in homogeneous isotropic turbulence

Ruetsch, G. R.; Maxey, Martin

doi:10.1063/1.858333

Cited by 104 publications

(64 citation statements)

References 27 publications

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“…[46]). There was no evidence in these data or those of Kaneda et al of KelvinHelmholtz billows forming as internal layers-as has been noted in simulations at low Reynolds number flow by Ruetsch & Maxey [47] or on certain boundary interfaces. Rather as the pdf of strain-vorticity diagrams demonstrate, the vortices were generated by large-scale straining motions as also observed in DNS.…”

Section: Interfaces With Turbulent Flowsmentioning

confidence: 44%

Interfaces and inhomogeneous turbulence

Hunt

Eames

Silva

et al. 2011

Phil. Trans. R. Soc. A.

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A Euromech colloquium, on interfacial processes and inhomogeneous turbulence, was held in London on 28-30 June 2010. Papers were presented describing and analysing the influence of interfaces that separate turbulent/non-turbulent regions, between regions of contrasting fluid properties, or at the edge of boundaries. This paper describes a summary of the work presented, giving a snapshot of the current progress in this area, along with discussions about future research directions.

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Section: Interfaces With Turbulent Flowsmentioning

confidence: 44%

Interfaces and inhomogeneous turbulence

Hunt

Eames

Silva

et al. 2011

Phil. Trans. R. Soc. A.

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“…Recent work has confirmed the existence of intermittently distributed sheet-like structures for scalar gradients (Ruetsch & Maxey 1992;Brethouwer, Hunt & Nieuwstadt 2003) or scalar variance dissipation (Schumacher, Sreenivasan & Yeung 2005). Some iso-contour plots can mimic geometry properties in Lagrangian turbulence but not in a rigorous sense, because there is no smallest scale in Lagrangian scalar dispersion without diffusion and the topology of iso-surfaces of the Lagrangian scalar must be invariant in evolution.…”

Section: Introductionmentioning

confidence: 99%

“…Because the passive scalar gradient tends to align with the most compressive strain direction in turbulent flow (e.g. Ashurst et al 1987;Ruetsch & Maxey 1992;Brethouwer et al 2003) and referring to (4.17), we hypothesize that in turbulent flow or the frozen turbulent flow,…”

Section: Transport Equations For Alignment Anglesmentioning

confidence: 99%

Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence

2010

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We report the multi-scale geometric analysis of Lagrangian structures in forced isotropic turbulence and also with a frozen turbulent field. A particle backwardtracking method, which is stable and topology preserving, was applied to obtain the Lagrangian scalar field φ governed by the pure advection equation in the Eulerian form ∂ t φ + u · ∇φ = 0. The temporal evolution of Lagrangian structures was first obtained by extracting iso-surfaces of φ with resolution 1024 3 at different times, from t = 0 to t = T e , where T e is the eddy turnover time. The surface area growth rate of the Lagrangian structure was quantified and the formation of stretched and rolled-up structures was observed in straining regions and stretched vortex tubes, respectively. The multi-scale geometric analysis of Bermejo-Moreno & Pullin (J. Fluid Mech., vol. 603, 2008, p. 101) has been applied to the evolution of φ to extract structures at different length scales and to characterize their non-local geometry in a space of reduced geometrical parameters. In this multi-scale sense, we observe, for the evolving turbulent velocity field, an evolutionary breakdown of initially large-scale Lagrangian structures that first distort and then either themselves are broken down or stretched laterally into sheets. Moreover, after a finite time, this progression appears to be insensible to the form of the initially smooth Lagrangian field. In comparison with the statistical geometry of instantaneous passive scalar and enstrophy fields in turbulence obtained by Bermejo-Moreno & Pullin (2008) and Bermejo-Moreno et al. (J. Fluid Mech., vol. 620, 2009, p. 121), Lagrangian structures tend to exhibit more prevalent sheet-like shapes at intermediate and small scales. For the frozen flow, the Lagrangian field appears to be attracted onto a stream-surface field and it develops less complex multi-scale geometry than found for the turbulent velocity field. In the latter case, there appears to be a tendency for the Lagrangian field to move towards a vortex-surface field of the evolving turbulent flow but this is mitigated by cumulative viscous effects.

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“…Furthermore, as Ruetsch & Maxey (1992) pointed out when studying the evolution of smallscale structures in incompressible homogeneous isotropic turbulence, vortex tubes and vortex sheets should not be considered as separate, independent structures. Instead, they form composite structures, as those shown in figure 27, with dependent geometries.…”

Section: Application To Structures Of ω I ω I and S Ij S Ijmentioning

confidence: 99%

Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

2009

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We perform a multi-scale non-local geometrical analysis of the structures extracted from the enstrophy and kinetic energy dissipation-rate, instantaneous fields of a numerical database of incompressible homogeneous isotropic turbulence decaying in time obtained by DNS in a periodic box. Three different resolutions are considered: 256 3 , 512 3 and 1024 3 grid points, with k maxη approximately 1, 2 and 4, respectively, the same initial conditions and Re λ ≈ 77. This allows a comparison of the geometry of the structures obtained for different resolutions. For the highest resolution, structures of enstrophy and dissipation evolve in a continuous distribution from blob-like and moderately stretched tube-like shapes at the large scales to highly stretched sheetlike structures at the small scales. The intermediate scales show a predominance of tube-like structures for both fields, much more pronounced for the enstrophy field. The dissipation field shows a tendency towards structures with lower curvedness than those of the enstrophy, for intermediate and small scales. The 256 3 grid resolution case (k maxη ≈ 1) was unable to detect the predominance of highly stretched sheet-like structures at the smaller scales in both fields. The same non-local methodology for the study of the geometry of structures, but without the multi-scale decomposition, is applied to two scalar fields used by existing local criteria for the eduction of tube-and sheet-like structures in turbulence, Q and [A ij ] + , respectively, obtained from invariants of the velocity-gradient tensor and alike in the 1024 3 case. This adds the non-local geometrical characterization and classification to those local criteria, assessing their validity in educing particular geometries. Finally, we introduce a new methodology for the study of proximity issues among structures of different fields, based on geometrical considerations and non-local analysis, by taking into account the spatial extent of the structures. We apply it to the four fields previously studied. Tube-like structures of Q are predominantly surrounded by sheet-like structures of [A ij ] + , which appear at closer distances. For the enstrophy, tube-like structures at an intermediate scale are primarily surrounded by sheets of smaller scales of the enstrophy and structures of dissipation at the same and smaller scales. A secondary contribution results from tubes of enstrophy at smaller scales appearing at farther distances. Different configurations of composite structures are presented.

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The evolution of small-scale structures in homogeneous isotropic turbulence

Cited by 104 publications

References 27 publications

Interfaces and inhomogeneous turbulence

Interfaces and inhomogeneous turbulence

Multi-scale geometric analysis of Lagrangian structures in isotropic turbulence

Geometry of enstrophy and dissipation, grid resolution effects and proximity issues in turbulence

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