Characterizing most irregular small-scale structures in turbulence using local Hölder exponents

Nguyen, Florian; Laval, Jean-Philippe; Dubrulle, Bérengère

doi:10.1103/physreve.102.063105

Cited by 10 publications

(6 citation statements)

References 33 publications

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“…Yet, there are still a few places where h is below 1 (see Figure 4b), so that the field is non-differentiable. The same procedure has been repeated for velocity fields in the inertial range, resulting in values of h even smaller than h = 1/3, see [44]. The probability distribution function for h that one can get from such plots (Figure 4b) coincides by construction with (∆x) C(h) .…”

Section: Connection With Multi-fractal Formalism and Construction Of ...mentioning

confidence: 92%

“…The most irregular structures of a given data set can be obtained by looking for places where the pseudo-Holder exponent takes its lowest value, and then analyzing the features of velocity and vorticity field around that place. This was done in [44] for DNS. In Figure 4d, we report a plot of the vorticity field in the experimental case.…”

Section: Observation Of Most Irregular Structurementioning

confidence: 99%

“…More generally, one finds that the most irregular structures laying around places of lower h are vorticity filaments. The corresponding "typical" structure can be obtained by conditional averaging, after suitable translation and rotation [44]. It is shown in Figure 5a.…”

Section: Observation Of Most Irregular Structurementioning

confidence: 99%

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Multi-Fractality, Universality and Singularity in Turbulence

Dubrulle

2022

Fractal Fract

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In most geophysical flows, vortices (or eddies) of all sizes are observed. In 1941, Kolmogorov devised a theory to describe the hierarchical organization of such vortices via a homogeneous self-similar process. This theory correctly explains the universal power-law energy spectrum observed in all turbulent flows. Finer observations however prove that this picture is too simplistic, owing to intermittency of energy dissipation and high velocity derivatives. In this review, we discuss how such intermittency can be explained and fitted into a new picture of turbulence. We first discuss how the concept of multi-fractality (invented by Parisi and Frisch in 1982) enables to generalize the concept of self-similarity in a non-homogeneous environment and recover a universality in turbulence. We further review the local extension of this theory, and show how it enables to probe the most irregular locations of the velocity field, in the sense foreseen by Lars Onsager in 1949. Finally, we discuss how the multi-fractal theory connects to possible singularities, in the real or in the complex plane, as first investigated by Frisch and Morf in 1981.

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Section: Connection With Multi-fractal Formalism and Construction Of ...mentioning

confidence: 92%

Section: Observation Of Most Irregular Structurementioning

confidence: 99%

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Multi-Fractality, Universality and Singularity in Turbulence

Dubrulle

2022

Fractal Fract

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“…In particular, the 'spottiness' of the flow and the coexistence of regions of high and low enstrophy can clearly be seen in figure 1(f), which shows the regions of most intense vorticity in the flow. In particular, it would be interesting to connect these aspects with recent results quantifying this intermittency in terms of multifractality [78][79][80][81].…”

Section: Discussionmentioning

confidence: 99%

Energy transfer and vortex structures: visualizing the incompressible turbulent energy cascade

McKeown,

Pumir,

Rubinstein

et al. 2023

New J. Phys.

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The transfer of kinetic energy from large to small scales is a hallmark of turbulent flows. Yet, a precise mechanistic description of this transfer, which is expected to occur via an energy cascade, is still missing. Several conceptually simple configurations with vortex tubes have been proposed as a testing ground to understand the energy cascade. Here, we focus on incompressible flows and compare the energy transfer occurring in a statistically steady homogeneous isotropic turbulent (HIT) flow with the generation of fine-scale motions in configurations involving vortex tubes. We start by filtering the velocity field in bands of wavenumbers distributed logarithmically, which allows us to study energy transfer in Fourier space and also visualize the energy cascade in real space. In the case of a statistically steady HIT flow at a moderate Reynolds number, our numerical results do not reveal any significant correlation between regions of intense energy transfers and vorticity or strain, filtered in corresponding wavenumber bands, nor any simple self-similar process. In comparison, in the transient turbulent flow obtained from the interaction between two antiparallel vortex tubes, we observe a qualitatively simpler organization of the intense structures, as well as of the energy transfer. However, the correlations between energy transfer and strain are small, and point to complicated dynamics of energy transfer. By imposing a structure at large scales consisting of antiparallel vortex tubes in a statistically steady flow, we observed a picture qualitatively similar to what was observed for the transient flow, but the energy transfer statistics do not reproduce the type of triadic interactions seen in HIT. These results indicate that the specific properties of the large-scale vortical structures affect the way energy is transferred, and may not be fully representative of HIT.

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“…Previous experimental [ 30 , 31 ] and numerical investigations [ 32 ] about the location of the structures with extreme local energy transfer showed that they are located near interactions (possibly reconnection) of Burgers vortices. Previous and recent high-resolution numerical simulations of reconnection of anti-parallel vorticity filaments [ 33 , 34 ] showed that the process is associated with the formation of a local cusp over each filament that could possibly lead to a singular behaviour [ 35 ].…”

Section: Dynamics Of a Pair Of Pinçonsmentioning

confidence: 99%

A Model of Interacting Navier–Stokes Singularities

Faller

Geneste²,

Dubrulle³

2022

Entropy

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We introduce a model of interacting singularities of Navier–Stokes equations, named pinçons. They follow non-equilibrium dynamics, obtained by the condition that the velocity field around these singularities obeys locally Navier–Stokes equations. This model can be seen as a generalization of the vorton model of Novikov that was derived for the Euler equations. When immersed in a regular field, the pinçons are further transported and sheared by the regular field, while applying a stress onto the regular field that becomes dominant at a scale that is smaller than the Kolmogorov length. We apply this model to compute the motion of a pair of pinçons. A pinçon dipole is intrinsically repelling and the pinçons generically run away from each other in the early stage of their interaction. At a late time, the dissipation takes over, and the dipole dies over a viscous time scale. In the presence of a stochastic forcing, the dipole tends to orientate itself so that its components are perpendicular to their separation, and it can then follow during a transient time a near out-of-equilibrium state, with forcing balancing dissipation. In the general case where the pinçons have arbitrary intensity and orientation, we observe three generic dynamics in the early stage: one collapse with infinite dissipation, and two expansion modes, the dipolar anti-aligned runaway and an anisotropic aligned runaway. The collapse of a pair of pinçons follows several characteristics of the reconnection between two vortex rings, including the scaling of the distance between the two components, following Leray scaling tc−t.

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Characterizing most irregular small-scale structures in turbulence using local Hölder exponents

Cited by 10 publications

References 33 publications

Multi-Fractality, Universality and Singularity in Turbulence

Multi-Fractality, Universality and Singularity in Turbulence

Energy transfer and vortex structures: visualizing the incompressible turbulent energy cascade

A Model of Interacting Navier–Stokes Singularities

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