New relations for correlation functions in Navier–Stokes turbulence

Falkovich, Gregory; Fouxon, Itzhak; Oz, Yaron

doi:10.1017/s0022112009993429

Cited by 65 publications

(91 citation statements)

References 32 publications

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“…Nevertheless, we can derive a sort of 4/5 law when we look at the trace of the two-point correlation function (i.e. the equation for the energy); see also Falkovich, Fouxon & Oz (2010). Let us also put back forcing and viscosity:…”

Section: Discussionmentioning

confidence: 99%

Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence

2013

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We investigate the transfer properties of energy and helicity fluctuations in fully developed homogeneous and isotropic turbulence by changing the nature of the nonlinear Navier-Stokes terms. We perform a surgery of all possible interactions, by keeping only those triads that have sign-definite helicity content. In order to do this, we apply an exact decomposition of the velocity field in a helical Fourier basis, as first proposed by Constantin & Majda (Commun. Math. Phys, vol. 115, 1988, p. 435) and exploited in great detail by Waleffe (Phys. Fluids A, vol. 4, 1992, p. 350), and we evolve the Navier-Stokes dynamics keeping only those velocity components carrying a well-defined (positive or negative) helicity. The resulting dynamics preserves translational and rotational symmetries but not mirror invariance. We give clear evidence that this three-dimensional homogeneous and isotropic chiral turbulence is characterized by a stationary inverse energy cascade with a spectrum E back (k) ∼ k −5/3 and by a direct helicity cascade with a spectrum E forw (k) ∼ k −7/3 . Our results are important to highlight the dynamics and statistics of those subsets of all possible Navier-Stokes interactions responsible for reversal events in the energy-flux properties, and demonstrate that the presence of an inverse energy cascade is not necessarily connected to a two-dimensionalization of the flow. We further comment on the possible relevance of such findings to flows of geophysical interest under rotations and in thin layers. Finally we propose other innovative numerical experiments that can be achieved by using a similar decimation of degrees of freedom.

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Section: Discussionmentioning

confidence: 99%

Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence

2013

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“…Figure 17 describes fluid flow for the same initial Reynolds and Mach numbers but an initial disturbance with n = 1. Somewhat surprisingly, the Kolmogorov power law E C ∼ k −5/3 , seems to be robust and holds also for large Mach number when the incompressible approximation is no longer valid [50].…”

Section: Jhep04(2018)065mentioning

confidence: 94%

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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“…relativistic turbulence (see also [30] for compressible non-relativistic turbulence). Our notation, however, will differ: quantities evaluated at the point r 2 will have a prime, while quantities evaluated at the point r 1 will not.…”

Section: Jhep12(2015)067mentioning

confidence: 99%

Scaling relations in two-dimensional relativistic hydrodynamic turbulence

Westernacher-Schneider

Lehner

2015

J. High Energ. Phys.

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We derive exact scaling relations for two-dimensional relativistic hydrodynamic turbulence in the inertial range of scales. We consider both the energy cascade towards large scales and the enstrophy cascade towards small scales. We illustrate these relations by numerical simulations of turbulent weakly compressible flows. Intriguingly, the fluid-gravity correspondence implies that the gravitational field in black hole/black brane spacetimes with anti-de Sitter asymptotics should exhibit similar scaling relations.

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New relations for correlation functions in Navier–Stokes turbulence

Cited by 65 publications

References 32 publications

Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence

Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence

Holographic turbulence in a large number of dimensions

Scaling relations in two-dimensional relativistic hydrodynamic turbulence

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