Singularities in fully developed turbulence

Shivamoggi, Bhimsen K.

doi:10.1016/j.physleta.2015.05.030

Cited by 7 publications

(8 citation statements)

References 49 publications

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“…This result is in concurrence with the phenomenalogically deduced result that divorticity in 2D FDT grows exponentially with time (Shivamoggi 2015), thanks to the global-in-time regular behavior of 2D Navier-Stokes solutions evolving from smooth initial data in the inviscid limit (Rose andSulem 1978, Gallagher andGallay 2005), and non-smooth initial data (Marchioro 1998). The Okubo-Weiss parameter Q is a measure of the relative importance of flow strain (Q > 0, hyperbolic) and vorticity (Q < 0, elliptic).…”

Section: Recasting the Okubo-weiss Criterion Via The Beltrami Conditionsupporting

confidence: 90%

“…Notwithstanding these caveats, when used cautiously, much useful information can nonetheless be gained from the Okubo-Weiss criterion, so exploration of the geometric aspects of this device are of interest. Motivated by this, in this paper, we therefore seek to motivate the Okubo-Weiss criterion via compatibility with previous results on the evolution in time of divorticity in 2D fully-developed turbulence (FDT) (Shivamoggi 2015). We will explore topological implications of the Okubo-Weiss criterion like its interpretations in terms of the intrinsic metric properties of the underlying vorticity manifold.…”

Section: Introductionmentioning

confidence: 91%

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The Okubo–Weiss criterion in hydrodynamic flows: geometric aspects and further extension

Shivamoggi¹,

Heijst²,

Kamp³

2022

Fluid Dyn. Res.

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The Okubo [5]-Weiss [6] criterion has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo-Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo-Weiss criterion and show the Okubo-Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the underlying vorticity manifold. The Okubo-Weiss criterion is reformulated in polar coordinates, and is validated via several examples including the Lamb- Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi- geostrophic (QG) flows. The Okubo-Weiss parameter is shown to remain robust under the -plane approximation to the Coriolis parameter. The Okubo-Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo-Weiss type criterion is formulated for 3D axisymmetric flows, and is validated via application to the round Landau-Squire Laminar jet flow.

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Section: Recasting the Okubo-weiss Criterion Via The Beltrami Conditionsupporting

confidence: 90%

Section: Introductionmentioning

confidence: 91%

The Okubo–Weiss criterion in hydrodynamic flows: geometric aspects and further extension

Shivamoggi¹,

Heijst²,

Kamp³

2022

Fluid Dyn. Res.

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“…In hydrodynamics or magnetohydrodynamic turbulence, as explained above, a very complex partition of the energy according to the scale is observed (She et al 1990;Frisch 1995;Shivamoggi 2015), and it was understood that this complexity was an effect of intermittency, that is a consequence of the extremely complex geometrical organization, or partition, of the support of the energy at small scales. Observationally, this was supported by the detection of strong velocity-shears at subparsec scale (Falgarone et al 2009).…”

Section: Canonical and Microcanonical Approaches To Multifractalitymentioning

confidence: 99%

Description of turbulent dynamics in the interstellar medium: multifractal-microcanonical analysis

Yahia

Schneider

Bontemps

et al. 2021

A&A

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Observations of the interstellar medium (ISM) show a complex density and velocity structure, which is in part attributed to turbulence. Consequently, the multifractal formalism should be applied to observation maps of the ISM in order to characterize its turbulent and multiplicative cascade properties. However, the multifractal formalism, even in its more advanced and recent canonical versions, requires a large number of realizations of the system, which usually cannot be obtained in astronomy. We present a self-contained introduction to the multifractal formalism in a "microcanonical" version, which allows us, for the first time, to compute precise turbulence characteristic parameters from a single observational map without the need for averages in a grand ensemble of statistical observables (e.g., a temporal sequence of images). We compute the singularity exponents and the singularity spectrum for both observations and magnetohydrodynamic simulations, which include key parameters to describe turbulence in the ISM. For the observations we focus on the 250 µm Herschel map of the Musca filament. Scaling properties are investigated using spatial 2D structure functions, and we apply a two-point log-correlation magnitude analysis over various lines of the spatial observation, which is known to be directly related to the existence of a multiplicative cascade under precise conditions. It reveals a clear signature of a multiplicative cascade in Musca with an inertial range from 0.05-0.65 pc. We show that the proposed microcanonical approach provides singularity spectra that are truly scale invariant, as required to validate any method used to analyze multifractality. The obtained singularity spectrum of Musca, which is sufficiently precise for the first time, is clearly not as symmetric as usually observed in log-normal behavior. We claim that the singularity spectrum of the ISM toward Musca features a more log-Poisson shape. Since log-Poisson behavior is claimed to exist when dissipation is stronger for rare events in turbulent flows, in contrast to more homogeneous (in volume and time) dissipation events, we suggest that this deviation from log-normality could trace enhanced dissipation in rare events at small scales, which may explain, or is at least consistent with, the dominant filamentary structure in Musca. Moreover, we find that subregions in Musca tend to show different multifractal properties: While a few regions can be described by a log-normal model, other regions have singularity spectra better fitted by a log-Poisson model. This strongly suggests that different types of dynamics exist inside the Musca cloud. We note that this deviation from log-normality and these differences between subregions appear only after reducing noise features, using a sparse edge-aware algorithm, which have the tendency to "log-normalize" an observational map. Implications for the star formation process are discussed. Our study establishes fundamental tools that will be applied to other galactic clouds and simulations in forthcom...

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“…The term representing baroclinic effects in the flow in this equation introduces a characteristic length scale, namely, the Rossby radius of deformation R 0 ≡ √ gH/f , into the problem (H being the depth of the ocean taken to be uniform and g being the acceleration due to gravity) 16 . Consequently, this problem exhibits some interesting departures from the properties of classical 2D turbulence (Shivamoggi [39], [41]).…”

Section: Quasi-geostrophic Relative Dispersionmentioning

confidence: 99%

Effects of compressibility on turbulent relative particle dispersion

Shivamoggi

2016

EPL

Self Cite

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In this paper, phenomenological developments are used to explore several aspects of the relative particle dispersion (RPD) in different physical fully-developed turbulence (FDT) situations. The role played by the FDT cascade physics underlying this process is investigated. Many of these aspects are motivated by previous laboratory experiment and numerical simulation results. These are, * spatial intermittency effects exhibiting, (a) reduction of RPD in 3D FDT, corroborating the numerical simulation results (Boffetta and Sokolov [11]); (b) prevalence of power-law scaling of RPD in 2D FDT enstrophy cascade (no matter how weak spatial intermittency effects are), corroborating the difficulty in observing Lin [12] exponentical scaling law in laboratory experiments (Jullien [13]); * quasi-geostrophic FDT aspects exhibiting an enhanced RPD in the baroclinic regime of the energy cascade and a negative eddy-viscosity development to shed some insight into this aspect;* quasi-geostrophic FDT aspects exhibiting particle clumping in the baroclinic regime of the enstrophy cascade; * reduction of RPD, development of the ballistic regime and particle clustering due to compressibility effects in FDT, corroborating the laboratory experiment and numerical simulation results (Cressman et al. [14]).These results are developed from the established scaling relations for the various physical FDT cases and are further validated via alternative dimensional/scaling developments for the various physical FDT cases similar to the one given for 3D FDT by Batchelor and Townsend [15].

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Singularities in fully developed turbulence

Abstract: openAccessArticle: Falsecover date: 2015-09-18pii: S0375-9601(15)00460-0Harvest Date: 2016-01-06 13:08:07issueName:Page Range: 1887-1887href scidir: http://www.sciencedirect.com/science/article/pii/S0375960115004600pubType

Cited by 7 publications

References 49 publications

The Okubo–Weiss criterion in hydrodynamic flows: geometric aspects and further extension

The Okubo–Weiss criterion in hydrodynamic flows: geometric aspects and further extension

Description of turbulent dynamics in the interstellar medium: multifractal-microcanonical analysis

Effects of compressibility on turbulent relative particle dispersion

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