Identification method for vortex sheet structures in turbulent flows

Horiuti, Kiyosi; Takagi, Yasunari

doi:10.1063/1.2147610

Cited by 58 publications

(73 citation statements)

References 17 publications

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“…Horiuti & Takagi (2005) stated that the most prominent characteristic feature of a vortex sheet is that the strain rate and the vorticity are highly correlated and their magnitudes comparably large. This correlation between strain rate and vorticity is one of the key reasons for positive enstrophy amplification to take place within these vortex sheets.…”

Section: Statistical Resultsmentioning

confidence: 99%

Amplification of enstrophy in the far field of an axisymmetric turbulent jet

Buxton

Ganapathisubramani

2010

J. Fluid Mech.

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The amplification of enstrophy is explored using cinematographic stereoscopic particle image velocimetry data. The enstrophy production rate is investigated by observation of the statistical tendency of the vorticity vector (ω) to align with the eigenvectors of the rate of strain tensor (e i ). Previous studies have shown that ω preferentially aligns with the intermediate strain-rate eigenvector (e 2 ) and is arbitrarily aligned with the extensive strain-rate eigenvector (e 1 ). This study shows, however, that the nature of enstrophy amplification, whether it is positive (enstrophy production) or negative (enstrophy destruction), is dictated by the alignment between ω and e 1 . Parallel alignment leads to enstrophy production (ω i S ij ω j > 0), whereas perpendicular alignment leads to enstrophy destruction (ω i S ij ω j < 0). In this way, the arbitrary alignment between ω and e 1 is the summation of the effects of enstrophy producing and enstrophy destroying regions. The structure of enstrophy production is also examined with regards to the intermediate strain-rate eigenvalue, s 2 . Enstrophy producing regions are found to be topologically 'sheet-forming', due to an extensive (positive) value of s 2 in these regions, whereas enstrophy destroying regions are found to be 'spotty'. Strong enstrophy producing regions are observed to occur in areas of strong local swirling as well as in highly dissipative regions. Instantaneous visualizations, produced from the volume of data created by Taylor's hypothesis, reveal that these 'sheet-like' strong enstrophy producing regions encompass the high enstrophy, strongly swirling 'worms'. These 'worms' induce high local strain fields leading to the formation of dissipation 'sheets', thereby revealing enstrophy production to be a complex interaction between rotation and strain -the skew-symmetric and symmetric components of the velocity gradient tensor, respectively.

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Section: Statistical Resultsmentioning

confidence: 99%

Amplification of enstrophy in the far field of an axisymmetric turbulent jet

Buxton

Ganapathisubramani

2010

J. Fluid Mech.

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“…Among the various local criteria found in the literature, here we consider those used in Horiuti & Takagi (2005) and HF for educing vortex tubes and sheets, which are outlined below. A point is considered to belong to a vortex tube core where the second invariant, Q, of the velocity-gradient tensor, ∂u i /∂x j , has a sufficiently large value.…”

Section: Local Identification Criteriamentioning

confidence: 99%

“…The database includes three different grid resolutions, allowing us to study how this parameter affects the geometry of educed structures and the validity of the traditional grid resolution criterion in DNS from a geometrical standpoint. In § 3, we combine the non-local methodology with two local criteria of identification of vortex tubes and sheets in turbulence (Horiuti & Takagi 2005) that are based on scalar fields obtained from the velocity-gradient tensor. An assessment of the geometries expected from those local criteria is done.…”

Section: Introductionmentioning

confidence: 99%

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

2009

Self Cite

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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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“…Similarly, for a two-dimensional vortex layer with uniform transverse gradient, as illustrated in Figure 23 vortex tubes and vortex sheets (see, e.g., [34,63]). …”

Section: The 45mentioning

confidence: 99%

Geometrical statistics and vortex structures in helical and nonhelical turbulences

2010

Physics of Fluids

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In this paper we conduct an analysis of the geometrical and vortical statistics in the small scales of helical and non-helical turbulence generated with direct numerical simulations. Using a filtering approach, the helicity flux from large scales to small scales is represented by the subgrid-scale (SGS) helicity dissipation. The SGS helicity dissipation is proportional to the product between the SGS stress tensor and the symmetric part of the filtered vorticity gradient, a tensor we refer to as the vorticity strain rate. We document the statistics of the vorticity strain rate, the vorticity gradient, and the dual vector corresponding to the anti-symmetric part of the vorticity gradient. These results provide new insights into the local structures of the vorticity field. We also study the relations between these quantities and vorticity, SGS helicity dissipation, SGS stress tensor, and other quantities. We observe that in both helical and non-helical turbulence: (1) there is a high probability to find the dual vector aligned with the intermediate eigenvector of the vorticity strain rate tensor; (2) vorticity tends to make an angle of 45 degrees with both the most contractive and the most extensive eigen-directions of the vorticity strain rate tensor; (3) the vorticity strain rate shows a preferred alignment configuration with the SGS stress tensor; (4) in regions with strong straining of the vortex lines, there is a negative correlation between the third order invariant of the vorticity gradient tensor and SGS helicity dissipation fluctuations. The correlation is qualitatively explained in terms of the self-induced motions of local vortex structures, which tend to wind up the vortex lines and generate SGS helicity dissipation. In helical turbulence, we observe that the joint probability density function of the second and third tensor invariants of the vorticity gradient displays skewed distributions, with the direction of skewness depending on the sign of helicity input. We also observe that the intermediate eigenvalue of the vorticity strain rate tensor is more probable to take negative values. These interesting observations, reported for the first time, call for further studies into their dynamical origins and implications.

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Identification method for vortex sheet structures in turbulent flows

Cited by 58 publications

References 17 publications

Amplification of enstrophy in the far field of an axisymmetric turbulent jet

Amplification of enstrophy in the far field of an axisymmetric turbulent jet

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

Geometrical statistics and vortex structures in helical and nonhelical turbulences

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