Fundamentals of pair diffusion in kinematic simulations of turbulence

Osborne, D. R.; Vassilicos, J. C.; Sung, K.; Haigh, Joanna D.

doi:10.1103/physreve.74.036309

Cited by 35 publications

(51 citation statements)

References 36 publications

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“…Thomson & Devenish (2005) argue for a t 9/2 -regime rather than the t 3 Richardson regime in KS. However, Osborne et al (2006) have confirmed Nicolleau & Yu (2004)'s observation that the Richardson law can be captured by KS in the scaling of the pair diffusivity even when it cannot be captured in the scaling of the mean square separation itself because of contaminations by the initial separation. The results of Thomson & Devenish (2005) are concerned with the mean square separation rather than with the pair diffusivity and use an adaptive time step which, as Osborne et al (2006) have shown, can be responsible for t 9/2 scalings.…”

Section: Introductionsupporting

confidence: 64%

Kinematic simulation for stably stratified and rotating turbulence

Nicolleau

Vassilicos

2008

Fluid Dyn. Res.

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The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the Rapid Distortion Theory to a Kinematic Simulation of the Boussinesq equation with a Coriolis term.Scalings for one-and two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers.Particular attention is given to the locality-in-scale hypothesis for two-particle diffusion in purely rotating turbulence both in the horizontal and the vertical directions. It is observed that both rotation and stratification decrease the pair diffusivity and improve the validity of the locality-in-scale hypothesis. In the case of stratification the range of scales over which the locality-in-scale hypothesis is observed is increased.It is found that rotation decreases the diffusion in the horizontal direction as well as, though to a much lesser extent, in the vertical direction.

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Section: Introductionsupporting

confidence: 64%

Kinematic simulation for stably stratified and rotating turbulence

Nicolleau

Vassilicos

2008

Fluid Dyn. Res.

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“…As well, approaches in Fourier modes are still widely used to study particle diffusion [2][3][4][5]26] in turbulent media. One can quote the development of the kinematic simulation (KS), which is very similar to Kraichnan's method [1].…”

Section: Doi: 102514/1j052368mentioning

confidence: 99%

“…Numerous studies in fields of application as diverse as particle diffusion [1][2][3][4][5], turbulence injection at the inlet boundary of unsteady calculations [6][7][8][9], or aeroacoustics [10][11][12][13][14][15] leaned upon stochastic methods to model the turbulence. This kind of approach presents the advantage of being easily applicable and less expensive than direct computations.…”

Section: Doi: 102514/1j052368mentioning

confidence: 99%

Turbulence Generation from a Sweeping-Based Stochastic Model

et al. 2014

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Stochastic methods are widely used because they constitute a low-cost computational-fluid-dynamics approach to synthesize a turbulent velocity field from time-averaged variables of a flowfield. A new combined stochastic method based on the sweeping hypothesis is introduced in this paper. This phenomenon, stating that inertial range structures are advected by the energy containing eddies, is known to be an important mechanism of the turbulent velocity field decorrelation process. The proposed method presents the advantage of being easily implementable and applicable to any three-dimensional configuration as long as a steady Reynolds-averaged Navier-Stokes computation of the flow is available and assuming that the considered turbulence physics is compatible with the hypotheses made to build the current numerical model. The developed method is applied on a subsonic round cold free jet. The validation study shows that the synthesized turbulent velocity fields reproduce statistical features of the flow, such as two-point twotime velocity correlation functions, comparable to those found experimentally and integrates shear effects of the mean flow. The mean convection velocity of the turbulent structures is also correctly modeled. In addition, the turbulent kinetic energy spatial distribution is preserved by the stochastic method.

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“…Thomson 39 argues that as a consequence and depending on the magnitude of the mean flow, ͗r͑t͒ 2 ͘ can grow in proportion to t 9/2 . The discussion is ongoing: Osborne et al 24 showed that while it is difficult to distinguish between regimes of ͗r 2 ͑t͒͘ ϰ t 3 and ͗r 2 ͑t͒͘ ϰ t 9/2 , even at very high Reynolds number, KS clearly reproduces Richardson's diffusion prediction d / dt͗r 2 ͑t͒͘ ϰ r 4/3 over a wide range of scales. In addition, Ref.…”

Section: Introductionmentioning

confidence: 99%

“…This situation calls for alternative tools to study the influence of such limitations. We mention the eddy-damped quasi-normal Markovian model ͑EDQNM͒, 22,23 the Lagrangian-history direct-interaction ͑LHDI͒ theory, 18 kinematic simulations ͑KS͒, [7][8][9]24 and the concept of persistent critical point flow patterns referred to as the statistical persistence hypothesis ͑SPH͒. 25,26 Yet another approach is the class of Lagrangian stochastic models ͑LSMs͒.…”

Section: Introductionmentioning

confidence: 99%

Self Similar Two Particle Separation Model

Lüthi¹,

Berg²,

Ott³

et al.

Springer Proceedings in Physics

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We present a new stochastic model for relative two-particle separation in turbulence. Inspired by material line stretching, we suggest that a similar process also occurs beyond the viscous range, with time scaling according to the longitudinal second-order structure function S 2 ͑r͒, e.g.; in the inertial range as −1/3 r 2/3 . Particle separation is modeled as a Gaussian process without invoking information of Eulerian acceleration statistics or of precise shapes of Eulerian velocity distribution functions. The time scale is a function of S 2 ͑r͒ and thus of the Lagrangian evolving separation. The model predictions agree with numerical and experimental results for various initial particle separations. We present model results for fixed time and fixed scale statistics. We find that for the Richardson-Obukhov law, i.e., ͗r͑t͒ 2 ͘ = g t 3 , to hold and to also be observed in experiments, high Reynolds numbers are necessary, i.e., Re Ͼ O͑1000͒, and the integral scale needs to be large compared to initial separation, i.e., L / r 0 Ͼ 30 and d / L Ͼ 3 need to be fulfilled, where d is the size of the field of view. Removing the constraint of finite inertial range, the model is used to explore separation dynamics in the asymptotic regime. As Re → ϱ, the distance neighbor function takes on a constant shape, almost as predicted by the Richardson diffusion equation. For the Richardson constant we obtain that g → 0.95 as Re → ϱ. This asymptotic limit is reached at Re Ͼ 1000. For the Richardson constant g, the model predicts a ratio of g b / g f Ϸ 1.9 between backwards and forwards dispersion.

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Fundamentals of pair diffusion in kinematic simulations of turbulence

Cited by 35 publications

References 36 publications

Kinematic simulation for stably stratified and rotating turbulence

Kinematic simulation for stably stratified and rotating turbulence

Turbulence Generation from a Sweeping-Based Stochastic Model

Self Similar Two Particle Separation Model

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