Eulerian vs Lagrangian Irreversibility in an Experimental Turbulent Swirling Flow

Cheminet, A.; Geneste, D.; Barlet, Antoine; Ostovan, Yaşar; Chaabo, Tarek; Valori, Valentina; Debue, Paul; Cuvier, Christophe; Daviaud, François; Foucaut, Jean-Marc; Laval, Jean-Philippe; Padilla, Vincent; Wiertel, Cécile; Dubrulle, Bérengère

doi:10.1103/physrevlett.129.124501

Cited by 7 publications

(4 citation statements)

References 31 publications

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“…It is an asymmetrical vorticity filament, with exponential vorticity profile corresponding to a Burgers vortex. Further investigation using time-resolved numerical [44] or experimental measurements [46] actually showed that the most irregular situations are obtained during vortex interaction, as illustrated in Figure 5b. More refined analysis prove that the interaction corresponds to vortex reconnection [47].…”

Section: Observation Of Most Irregular Structurementioning

confidence: 94%

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: Observation Of Most Irregular Structurementioning

confidence: 94%

Multi-Fractality, Universality and Singularity in Turbulence

Dubrulle

2022

Fractal Fract

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“…This property prescribes the 'arrow-of-time' of the irreversible Navier-Stokes dynamics and it is plausible that a similar property carries over to dissipative weak Euler solutions obtained in the inviscid limit (Eyink 2006). The dissipative anomaly for Navier-Stokes turbulence may be characterised also in terms of the time asymmetry of separation of stochastic Lagrangian particle (Drivas 2019;Cheminet et al 2022), which in three dimensions separate faster backwards in time than they do forwards in time (Eyink 2011;Buaria et al 2016).…”

Section: Origin Of Singularitiesmentioning

confidence: 85%

“…The dissipative anomaly for Navier–Stokes turbulence may be characterised also in terms of the time asymmetry of separation of stochastic Lagrangian particle (Drivas 2019; Cheminet et al. 2022), which in three dimensions separate faster backwards in time than they do forwards in time (Eyink 2011; Buaria et al. 2016).…”

Section: Turbulence Away From Wallsmentioning

confidence: 99%

Onsager's ‘ideal turbulence’ theory

Eyink

2024

J. Fluid Mech.

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In 1945–1949, Lars Onsager made an exact analysis of the high-Reynolds-number limit for individual turbulent flow realisations modelled by incompressible Navier–Stokes equations, motivated by experimental observations that dissipation of kinetic energy does not vanish. I review here developments spurred by his key idea that such flows are well described by distributional or ‘weak’ solutions of ideal Euler equations. 1/3 Hölder singularities of the velocity field were predicted by Onsager and since observed. His theory describes turbulent energy cascade without probabilistic assumptions and yields a local, deterministic version of the Kolmogorov $4/5$ th law. The approach is closely related to renormalisation group methods in physics and envisages ‘conservation-law anomalies’, as discovered later in quantum field theory. There are also deep connections with large-eddy simulation modelling. More recently, dissipative Euler solutions of the type conjectured by Onsager have been constructed and his $1/3$ Hölder singularity proved to be the sharp threshold for anomalous dissipation. This progress has been achieved by an unexpected connection with work of John Nash on isometric embeddings of low regularity or ‘convex integration’ techniques. The dissipative Euler solutions yielded by this method are wildly non-unique for fixed initial data, suggesting ‘spontaneously stochastic’ behaviour of high-Reynolds-number solutions. I focus in particular on applications to wall-bounded turbulence, leading to novel concepts of spatial cascades of momentum, energy and vorticity to or from the wall as deterministic, space–time local phenomena. This theory thus makes testable predictions and offers new perspectives on large-eddy simulation in the presence of solid walls.

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“…Finally, by the experiments by Meneveau and Sreenivasan [39][40][41], assuming their flows remain bounded with increasing Reynolds number, the dimension of support of anomalous dissipation is 0.87 above our lower bound, indicating that -unlike the simple shock singularities and mathematical constructions -incompressible turbulence does not sit at the lower threshold of our theorem. It would be interesting to obtain additional experimental and numerical measurements of the spacetime support of the dissipation, perhaps leveraging a Lagrangian interpretation [5,12].…”

Section: Theorem 12 (Incompressible Euler)mentioning

confidence: 99%

On the Support of Anomalous Dissipation Measures

Rosa¹,

Drivas²,

Inversi³

2023

Preprint

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By means of a unifying measure-theoretic approach, we establish lower bounds on the Hausdorff dimension of the space-time set which can support anomalous dissipation for weak solutions of fluid equations, both in the presence or absence of a physical boundary. Boundary dissipation, which can occur at both the time and the spatial boundary, is analyzed by suitably modifying the Duchon & Robert interior distributional approach. One implication of our results is that any bounded Euler solution (compressible or incompressible) arising as a zero viscosity limit of Navier-Stokes solutions cannot have anomalous dissipation supported on a set of dimension smaller than that of the space. This result is sharp, as demonstrated by entropy-producing shock solutions of compressible Euler [14,36] and by recent constructions of dissipative incompressible Euler solutions [1, 2], as well as passive scalars [9,13]. For L q t L r x suitable Leray-Hopf solutions of the d−dimensional Navier-Stokes equation we prove a bound of the dissipation in terms of the Parabolic Hausdorff measure P s , which gives s = 1 as soon as the solution lies in the Prodi-Serrin class. In the three-dimensional case, this matches with the Caffarelli-Kohn-Nirenberg partial regularity.

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Eulerian vs Lagrangian Irreversibility in an Experimental Turbulent Swirling Flow

Cited by 7 publications

References 31 publications

Multi-Fractality, Universality and Singularity in Turbulence

Multi-Fractality, Universality and Singularity in Turbulence

Onsager's ‘ideal turbulence’ theory

On the Support of Anomalous Dissipation Measures

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