Longitudinal and transverse structure functions in high-Reynolds-number turbulence

Grauer, Rainer; Homann, Holger; Pinton, Jean‐François

doi:10.1088/1367-2630/14/6/063016

Cited by 31 publications

(42 citation statements)

References 22 publications

(48 reference statements)

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“…The present velocity field (1.8) is an example of random process that exhibits a higher level of intermittency for the transverse case than for the longitudinal case. This is indeed a surprising effect, also observed in real flows (see discussions in Chen et al (1997), Dhruva, Tsuji & Sreenivasan (1997), Grauer, Homann & Pinton (2012)). In our model, only an analytical study could give a clear answer to this observed discrepancy, in particular in the asymptotic limit → 0.…”

Section: Numerical Estimationssupporting

confidence: 61%

A dissipative random velocity field for fully developed fluid turbulence

2016

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We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent flow. A key step in the construction of this model is the introduction of some aspects of the vorticity stretching mechanism that governs the dynamics of fluid particles along their trajectory. An additional further phenomenological step aimed at including the long range correlated nature of turbulence makes this model depending on a single free parameter $\gamma$ that can be estimated from experimental measurements. We confirm the realism of the model regarding the geometry of the velocity gradient tensor, the power-law behaviour of the moments of velocity increments (i.e. the structure functions), including the intermittent corrections, and the existence of energy transfers across scales. We quantify the dependence of these basic properties of turbulent flows on the free parameter $\gamma$ and derive analytically the spectrum of exponents of the structure functions in a simplified non dissipative case. A perturbative expansion in power of $\gamma$ shows that energy transfers, at leading order, indeed take place, justifying the dissipative nature of this random field.Comment: 38 pages, 5 figure

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Section: Numerical Estimationssupporting

confidence: 61%

A dissipative random velocity field for fully developed fluid turbulence

2016

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“…The scaling exponents for second-order structure functions of δu r and δv r are indeed the same, but higher-order quantities can scale differently in principle [4], so there is no a priori assurance of principle that universality holds. The majority of the empirical evidence available, both experimental and numerical, shows that longitudinal and transverse structure functions indeed scale differently at higher orders [5][6][7][8][9][10][11][12][13], though some studies suggest otherwise [14,15]. Predicated on the consensus that the longitudinal and transverse structure functions scale differently, it was argued in Ref.…”

Section: Introductionmentioning

confidence: 99%

Reynolds number scaling of velocity increments in isotropic turbulence

2017

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Using the largest database of isotropic turbulence available to date, generated by the direct numerical simulation (DNS) of the Navier-Stokes equations on an 8192 3 periodic box, we show that the longitudinal and transverse velocity increments scale identically in the inertial range. By examining the DNS data at several Reynolds numbers, we infer that the contradictory results of the past on the inertial-range universality are artifacts of low Reynolds number and residual anisotropy. We further show that both longitudinal and transverse velocity increments scale on locally averaged dissipation rate, just as postulated by Kolmogorov's refined similarity hypothesis, and that, in isotropic turbulence, a single independent scaling adequately describes fluid turbulence in the inertial range.

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“…Table I summarizes the parameters of the simulations (see Ref. [19] for more details). In each case, the flow is seeded with 10 7 Lagrangian tracers.…”

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confidence: 99%

Time scales of turbulent relative dispersion

2012

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Tracers in a turbulent flow separate according to the celebrated t3/2 Richardson-Obukhov law, which is usually explained by a scale-dependent effective diffusivity. Here, supported by state-of-the-art numerics, we revisit this argument. The Lagrangian correlation time of velocity differences increases too quickly for validating this approach, but acceleration differences decorrelate on dissipative time scales. Phenomenological arguments are used to relate the behavior of separations to that of a "local energy dissipation," defined as the average ratio between the cube of the longitudinal velocity difference and the distance between the two tracers. This quantity is shown to stabilize on short time scales and this results in an asymptotic diffusion ∝t1/2 of velocity differences. The time of convergence to this regime is shown to be that of deviations from Batchelor's initial ballistic regime, given by a scale-dependent energy dissipation time rather than the usual turnover time. It is finally demonstrated that the fluid flow intermittency should not affect this long-time behavior of the relative motion.

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Longitudinal and transverse structure functions in high-Reynolds-number turbulence

Cited by 31 publications

References 22 publications

A dissipative random velocity field for fully developed fluid turbulence

A dissipative random velocity field for fully developed fluid turbulence

Reynolds number scaling of velocity increments in isotropic turbulence

Time scales of turbulent relative dispersion

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