Anomalous scaling and universality in hydrodynamic systems with power-law forcing

Biferale, Luca; Cencini, Massimo; Lanotte, Alessandra S.; Sbragaglia, Mauro; Toschi, Federico

doi:10.1088/1367-2630/6/1/037

Cited by 31 publications

(30 citation statements)

References 46 publications

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“…Nevertheless, this randomly forced model has played an important role historically. Thus it has been studied numerically via the pseudo-spectral method [119,120]. These studies have shown that, even though the stochastic forcing destroys the vorticity tubes that we have described above, it yields multiscaling of velocity structure that is consistent, for y = 4, with the analogous multiscaling in the conventional 3D Navier-Stokes equation, barring logarithmic corrections.…”

Section: D Navier-stokes Turbulencementioning

confidence: 94%

Statistical properties of turbulence: An overview

2009

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Section: D Navier-stokes Turbulencementioning

confidence: 94%

Statistical properties of turbulence: An overview

2009

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“…For 0 < ε < 2, these results are also consistent with the direct numerical simulations of Refs. [19,20].…”

Section: A Simplified Modelmentioning

confidence: 99%

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

Mejía‐Monasterio

Muratore-Ginanneschi

2012

Phys. Rev. E

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We study the renormalization group flow of the average action of the stochastic Navier-Stokes equation with power-law forcing. Using Galilean invariance, we introduce a nonperturbative approximation adapted to the zero-frequency sector of the theory in the parametric range of the Hölder exponent 4 − 2 ε of the forcing where real-space local interactions are relevant. In any spatial dimension d, we observe the convergence of the resulting renormalization group flow to a unique fixed point which yields a kinetic energy spectrum scaling in agreement with canonical dimension analysis. Kolmogorov's −5/3 law is, thus, recovered for ε = 2 as also predicted by perturbative renormalization. At variance with the perturbative prediction, the −5/3 law emerges in the presence of a saturation in the ε dependence of the scaling dimension of the eddy diffusivity at ε = 3/2 when, according to perturbative renormalization, the velocity field becomes infrared relevant.

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“…It is therefore difficult to decide whether or not the saturation occurs. As discussed in [44], one can understand the curvature of the local slopes with the presence of sub-dominant terms, e.g., with the superposition of two power laws P 2 (r) ≃ Ar a + Br b . In our case, one can expect that…”

Section: A Saturation Of the Correlation Dimensionmentioning

confidence: 99%

Stochastic suspensions of heavy particles

Bec

Cencini

Hillerbrand

et al. 2008

Physica D: Nonlinear Phenomena

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Turbulent suspensions of heavy particles in incompressible flows have gained much attention in recent years. A large amount of work focused on the impact that the inertia and the dissipative dynamics of the particles have on their dynamical and statistical properties. Substantial progress followed from the study of suspensions in model flows which, although much simpler, reproduce most of the important mechanisms observed in real turbulence. This paper presents recent developments made on the relative motion of a pair of particles suspended in time-uncorrelated and spatially self-similar Gaussian flows. This review is complemented by new results. By introducing a time-dependent Stokes number, it is demonstrated that inertial particle relative dispersion recovers asymptotically Richardson's diffusion associated to simple tracers. A perturbative (homogeneization) technique is used in the small-Stokes-number asymptotics and leads to interpreting first-order corrections to tracer dynamics in terms of an effective drift. This expansion implies that the correlation dimension deficit behaves linearly as a function of the Stokes number. The validity and the accuracy of this prediction is confirmed by numerical simulations.

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Anomalous scaling and universality in hydrodynamic systems with power-law forcing

Cited by 31 publications

References 46 publications

Statistical properties of turbulence: An overview

Statistical properties of turbulence: An overview

Nonperturbative renormalization group study of the stochastic Navier-Stokes equation

Stochastic suspensions of heavy particles

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