The decay of homogeneous anisotropic turbulence

Biferale, Luca; Boffetta, G.; Celani, Antonio; Lanotte, Alessandra S.; Toschi, Federico; Vergassola, Massimo

doi:10.1063/1.1582859

Cited by 38 publications

(47 citation statements)

References 28 publications

(69 reference statements)

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“…Little is known about the behavior of turbulence that is driven like this. The direction and degree of energy transfer and the morphology of the resulting flow could be greatly affected by the type and scale of energy input (see Biferale et al 2004). However, it appears that for average disk conditions the power input is dominated by cluster winds or superbubbles with an injection scale of ∼ 50 − 500 pc.…”

Section: Power Sources For Interstellar Turbulencementioning

confidence: 99%

Interstellar Turbulence I: Observations and Processes

Elmegreen

Scalo

2004

Annu. Rev. Astron. Astrophys.

1,115

983

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Turbulence affects the structure and motions of nearly all temperature and density regimes in the interstellar gas. This two-part review summarizes the observations, theory, and simulations of interstellar turbulence and their implications for many fields of astrophysics. The first part begins with diagnostics for turbulence that have been applied to the cool interstellar medium, and highlights their main results. The energy sources for interstellar turbulence are then summarized along with numerical estimates for their power input. Supernovae and superbubbles dominate the total power, but many other sources spanning a large range of scales, from swing amplified gravitational instabilities to cosmic ray streaming, all contribute in some way. Turbulence theory is considered in detail, including the basic fluid equations, solenoidal and compressible modes, global inviscid quadratic invariants, scaling arguments for the power spectrum, phenomenological models for the scaling of higher order structure functions, the direction and locality of energy transfer and cascade, velocity probability distributions, and turbulent pressure. We emphasize expected differences between incompressible and compressible turbulence. Theories of magnetic turbulence on scales smaller than the collision mean free path are included, as are theories of magnetohydrodynamic turbulence and their various proposals for power spectra. Numerical simulations of interstellar turbulence are reviewed. Models have reproduced the basic features of the observed scaling relations, predicted fast decay rates for supersonic MHD turbulence, and derived probability distribution functions for density. Thermal instabilities and thermal phases have a new interpretation in a supersonically turbulent medium. Large-scale models with various combinations of self-gravity, magnetic fields, supernovae, and -2 -star formation are beginning to resemble the observed interstellar medium in morphology and statistical properties. The role of self-gravity in turbulent gas evolution is clarified, leading to new paradigms for the formation of star clusters, the stellar mass function, the origin of stellar rotation and binary stars, and the effects of magnetic fields. The review ends with a reflection on the progress that has been made in our understanding of the interstellar medium, and offers a list of outstanding problems.

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Section: Power Sources For Interstellar Turbulencementioning

confidence: 99%

Interstellar Turbulence I: Observations and Processes

Elmegreen

Scalo

2004

Annu. Rev. Astron. Astrophys.

1,115

983

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“…The 1941 theory of Kolmogorov [1] is based on the assumption of local isotropy and homogeneity, that is any turbulent flow, independently on the injection mechanism, recovers universal statistical properties, for scales small enough (and far from the boundaries). Indeed, experiments and numerical simulations give strong indications that Eulerian and Lagrangian isotropic/anisotropic small-scales velocity statistics are pretty independent of the large-scale forcing mechanisms [3][4][5][6][7]. Still, we lack a firm understanding for these evidences.…”

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confidence: 99%

“…The two top curves are for y = 3.5 at the two resolutions 256 3 and 512 3 : they are compensated with the dimensional scaling 4, i.e. with an exponent α = ζ (6) y=3.5 = 0.5. The bottom curve refers to the case y = 6, at the resolutions 256 3 , and is also compensated with the exponent for the scaling (4), α = ζ (6) y=6 = 6.…”

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confidence: 99%

Effects of Forcing in Three-Dimensional Turbulent Flows

2004

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We present the results of a numerical investigation of three-dimensional homogeneous and isotropic turbulence, stirred by a random forcing with a power law spectrum, E f (k) ∼ k 3−y . Numerical simulations are performed at different resolutions up to 512 3 . We show that at varying the spectrum slope y, small-scale turbulent fluctuations change from a forcing independent to a forcing dominated statistics. We argue that the critical value separating the two behaviours, in three dimensions, is yc = 4. When the statistics is forcing dominated, for y < yc, we find dimensional scaling, i.e. intermittency is vanishingly small. On the other hand, for y > yc, we find the same anomalous scaling measured in flows forced only at large scales. We connect these results with the issue of universality in turbulent flows.The effects of both external forcing mechanisms and boundary conditions on small-scale turbulent fluctuations have been the subject of many theoretical, numerical and experimental studies [1,2]. The 1941 theory of Kolmogorov [1] is based on the assumption of local isotropy and homogeneity, that is any turbulent flow, independently on the injection mechanism, recovers universal statistical properties, for scales small enough (and far from the boundaries). Indeed, experiments and numerical simulations give strong indications that Eulerian and Lagrangian isotropic/anisotropic small-scales velocity statistics are pretty independent of the large-scale forcing mechanisms [3][4][5][6][7]. Still, we lack a firm understanding for these evidences. From the theoretical point of view, precious hints arise from linear problems, like passive scalar or passively advected magnetic fields. For the class of Kraichnan models [8], anomalous scaling has been shown to be associated to statistically stationary solutions of the unforced equations for correlation functions [9]. Scaling exponents are consequently universal with respect of the injection mechanisms. Concerning non-linear problems, as the Navier-Stokes case, analytical results have been often pursued by means of the Renormalization Group (RG) [10,11]. In the RG framework, turbulence is stirred at all scales by a self-similar Gaussian field, with zero mean and white-noise in time. The two-point correlation function in Fourier space is given byHere 1/k 0 ∼ L is the largest length in the system (infrared cut-off), D 0 is the forcing intensity, P ij (k) is the projector assuring incompressibility and d is the spatial dimension (always assumed to be d = 3 hereafter). The influence of the stirring mechanism at small scales is governed by the value of the slope y. We go from a situation when the forcing has a strong input at all scales, y ∼ 0 originally investigated in [10], to a quasi large-scale forcing when y → ∞. Renormalization Group calculations, based on a y-expansion, predict a power-law energy spec-where η is the viscous scale of the system, and for y ≪ 1. Notice that the Kolmogorov value, E(k) ∼ k −5/3 , describing experimental turbulent flows stirred by a largescale fo...

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“…Nevertheless the universality of C 2 and C p for p ≤ 4 is still under debate. For example, very recently in [17] the authors argued on the basis of a 256 3 DNS "in favor of an "exponents only" universality scenario for forced turbulence".…”

Section: Introductionmentioning

confidence: 99%

Strong universality in forced and decaying turbulence in a shell model

et al. 2003

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The weak version of universality in turbulence refers to the independence of the scaling exponents of the nth order strcuture functions from the statistics of the forcing. The strong version includes universality of the coefficients of the structure functions in the isotropic sector, once normalized by the mean energy flux. We demonstrate that shell models of turbulence exhibit strong universality for both forced and decaying turbulence. The exponents and the normalized coefficients are time independent in decaying turbulence, forcing independent in forced turbulence, and equal for decaying and forced turbulence. We conjecture that this is also the case for Navier-Stokes turbulence.

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The decay of homogeneous anisotropic turbulence

Cited by 38 publications

References 28 publications

Interstellar Turbulence I: Observations and Processes

Interstellar Turbulence I: Observations and Processes

Effects of Forcing in Three-Dimensional Turbulent Flows

Strong universality in forced and decaying turbulence in a shell model

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