Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence

Eyink, Gregory L.; Drivas, Theodore D.

doi:10.1103/physrevx.8.011023

Cited by 28 publications

(35 citation statements)

References 110 publications

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“…Our analysis of compressible Navier-Stokes and Euler solutions was directly motivated by the earlier work of Aluie [29], and our theorems generalize previous results for barotropic compressible flow [10]. It is worth noting that all of our results generalize to relativistic Euler equations in Minkowski spacetime, following the discussion in [30].…”

Section: Introductionsupporting

confidence: 64%

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

Drivas

Eyink

2017

Commun. Math. Phys.

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We prove that bounded weak solutions of the compressible Euler equations will conserve thermodynamic entropy unless the solution fields have sufficiently low space-time Besov regularity. A quantity measuring kinetic energy cascade will also vanish for such Euler solutions, unless the same singularity conditions are satisfied. It is shown furthermore that strong limits of solutions of compressible Navier-Stokes equations that are bounded and exhibit anomalous dissipation are weak Euler solutions. These inviscid limit solutions have nonnegative anomalous entropy production and kinetic energy dissipation, with both vanishing when solutions are above the critical degree of Besov regularity. Stationary, planar shocks in Euclidean space with an ideal-gas equation of state provide simple examples that satisfy the conditions of our theorems and which demonstrate sharpness of our L 3 -based conditions. These conditions involve space-time Besov regularity, but we show that they are satisfied by Euler solutions that possess similar space regularity uniformly in time.

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Section: Introductionsupporting

confidence: 64%

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

Drivas

Eyink

2017

Commun. Math. Phys.

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“…By means of this intuitive but rigorous approach, we shall resolve the controversies concerning nonrelativistic compressible fluid turbulence. In a companion paper, we further extend our analysis to relativistic fluid turbulence [48].…”

Section: Introductionmentioning

confidence: 93%

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

Eyink

Drivas

2018

Phys. Rev. X

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We investigate dissipative anomalies in a turbulent fluid governed by the compressible Navier-Stokes equation. We follow an exact approach pioneered by Onsager, which we explain as a nonperturbative application of the principle of renormalization-group invariance. In the limit of high Reynolds and Péclet numbers, the flow realizations are found to be described as distributional or "coarse-grained" solutions of the compressible Euler equations, with standard conservation laws broken by turbulent anomalies. The anomalous dissipation of kinetic energy is shown to be due not only to local cascade, but also to a distinct mechanism called pressure-work defect. Irreversible heating in stationary, planar shocks with an ideal-gas equation of state exemplifies the second mechanism. Entropy conservation anomalies are also found to occur by two mechanisms: an anomalous input of negative entropy (negentropy) by pressure-work and a cascade of negentropy to small scales. We derive "4/5th-law"-type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required to sustain the cascades. We compare our approach with alternative theories and empirical evidence. It is argued that the "Big Power-Law in the Sky" observed in electron density scintillations in the interstellar medium is a manifestation of a forward negentropy cascade, or an inverse cascade of usual thermodynamic entropy. arXiv:1704.03532v1 [physics.flu-dyn]

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“…There has been some work on the analytical front [1,22,23] and several numerical investigations [1,13,[24][25][26][27][28][29][30][31]. Because correlation functions can indeed be measured in relevant scenarios -perhaps even in QG plasma [8,9,[32][33][34] -and interesting implications for the gravitational field follow from holography, it is of interest to further investigate relativistic turbulence.…”

Section: Jhep08(2017)027mentioning

confidence: 99%

Numerical measurements of scaling relations in two-dimensional conformal fluid turbulence

Westernacher-Schneider

Lehner

2017

J. High Energ. Phys.

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We present measurements of relativistic scaling relations in (2+1)-dimensional conformal fluid turbulence from direct numerical simulations, in the weakly compressible regime. These relations were analytically derived previously in [1] for a relativistic fluid; this work is a continuation of that study, providing further analytical insights together with numerical experiments to test the scaling relations and extract other important features characterizing the turbulent behavior. We first explicitly demonstrate that the nonrelativistic limit of these scaling relations reduce to known results from the statistical theory of incompressible Navier-Stokes turbulence. In simulations of the inverse-cascade range, we find the relevant relativistic scaling relation is satisfied to a high degree of accuracy. We observe that the non-relativistic versions of this scaling relation underperform the relativistic one in both an absolute and relative sense, with a progressive degradation as the rms Mach number increases from 0.14 to 0.19. In the direct-cascade range, the two relevant relativistic scaling relations are satisfied with a lower degree of accuracy in a simulation with rms Mach number 0.11. We elucidate the poorer agreement with further simulations of an incompressible Navier-Stokes fluid. Finally, as has been observed in the incompressible Navier-Stokes case, we show that the energy spectrum in the inversecascade of the conformal fluid exhibits k −2 scaling rather than the Kolmogorov/Kraichnan expectation of k −5/3 , and that it is not necessarily associated with compressive effects. We comment on the implications for a recent calculation of the fractal dimension of a turbulent (3 + 1)-dimensional AdS black brane.

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Cascades and Dissipative Anomalies in Relativistic Fluid Turbulence

Cited by 28 publications

References 110 publications

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

An Onsager Singularity Theorem for Turbulent Solutions of Compressible Euler Equations

Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

Numerical measurements of scaling relations in two-dimensional conformal fluid turbulence

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