Scaling relations in two-dimensional relativistic hydrodynamic turbulence

Westernacher-Schneider, John Ryan; Lehner, Luis; Oz, Yaron

doi:10.1007/jhep12(2015)067

Cited by 20 publications

(50 citation statements)

References 39 publications

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“…This includes the use of a random external force to generate the turbulent flow, as well as considerations specific to simulating either a conformal fluid or an incompressible Navier-Stokes fluid. The equivalence between previously known results and the incompressible limit of the scaling relations derived in [1] is explicitly demonstrated. We give our results in section 4, where our numerical measurements of the scaling relations derived in [1] are presented.…”

Section: Jhep08(2017)027supporting

confidence: 58%

“…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%

“…In the current work we measure scaling relations in (2 + 1)-dimensional relativistic conformal fluids in the weakly-compressible turbulent regime and compare them to the predictions in [1] and various limits thereof. The (2 + 1)-dimensional case is especially relevant to draw intuition for related phenomena in (3 + 1)-dimensional gravity with the help of the fluid-gravity correspondence (e.g.…”

Section: Jhep08(2017)027mentioning

confidence: 99%

“…[12,16,25]). This work is largely a continuation and completion of [1], which contained a numerical study which was inconclusive at the time.…”

Section: Jhep08(2017)027mentioning

confidence: 99%

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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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Section: Jhep08(2017)027supporting

confidence: 58%

Section: Jhep08(2017)027mentioning

confidence: 99%

Section: Jhep08(2017)027mentioning

confidence: 99%

“…[12,16,25]). This work is largely a continuation and completion of [1], which contained a numerical study which was inconclusive at the time.…”

Section: Jhep08(2017)027mentioning

confidence: 99%

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

Westernacher-Schneider

Lehner

2017

J. High Energ. Phys.

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“…A recent review which examines both hydrodynamic and magnetohydrodynamic implementations of supersonic compressible turbulence on statistical quantities can be found in Falceta-Goncalves et al (2014). In this work, we follow the vast majority of investigations (Kuznetsov and Sereshchenko, 2015;Shivamoggi, 2015;Domaradzki and Carati, 2007;Sun, 2016;Westernacher-Schneider et al, 2015;Ottaviani, 1992;Qiu et al, 2016;Bershadskii, 2016) by utilizing the phenomenological description of turbulence 15 in Fourier space as well as the utilization of two-point velocity structure functions for the statistical examination of our high fidelity numerical simulations. In terms of reference scaling behavior, we shall be comparing our numerical results against the theories advanced in Shivamoggi (1992) under the assumption of isentropic flow.…”

Section: Introductionmentioning

confidence: 99%

Stratified Kelvin-Helmholtz turbulence of compressible shear flows

Maulik¹,

San²

2018

Preprint

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Abstract. We study the scaling laws and structure functions of stratified shear flows by performing high-resolution numerical simulations of inviscid compressible turbulence induced by Kelvin-Helmholtz instability. An implicit large eddy simulation approach is adapted to solve our conservation laws for both two-dimensional (with a spatial resolution of 16, 3842 ) and threedimensional (with a spatial resolution of 512 3 ) configurations utilizing different compressibility characteristics such as shocks.For three-dimensional turbulence, we find that both kinetic energy and density-weighted energy spectra follow the classical 5

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Holographic turbulence in a large number of dimensions

Rozali

Sabag

Yarom

2018

J. High Energ. Phys.

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Abstract:We consider relativistic hydrodynamics in the limit where the number of spatial dimensions is very large. We show that under certain restrictions, the resulting equations of motion simplify significantly. Holographic theories in a large number of dimensions satisfy the aforementioned restrictions and their dynamics are captured by hydrodynamics with a naturally truncated derivative expansion. Using analytic and numerical techniques we analyze two and three-dimensional turbulent flow of such fluids in various regimes and its relation to geometric data.

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Scaling relations in two-dimensional relativistic hydrodynamic turbulence

Cited by 20 publications

References 39 publications

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

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

Stratified Kelvin-Helmholtz turbulence of compressible shear flows

Holographic turbulence in a large number of dimensions

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