Turbulent diffusion in stably stratified non-decaying turbulence

Nicolleau, F.; Vassilicos, J. C.

doi:10.1017/s0022112099008113

Cited by 39 publications

(69 citation statements)

References 19 publications

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“…As a result, a plateau is found for single-particle dispersion in the vertical direction, which scales proportional to N −2 with N the buoyancy frequency. 1,2 This plateau is reached for intermediate times, around t =2 / N. In the present work, this plateau is found too, but moreover we find a diffusive regime for long times. The effect of stratification on horizontal dispersion is not clear yet, often it is assumed to be similar to dispersion in homogeneous isotropic turbulence.…”

Section: Introductionsupporting

confidence: 73%

Single-particle, particle-pair, and multiparticle dispersion of fluid particles in forced stably stratified turbulence

2008

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The dispersion of fluid particles in statistically stationary stably stratified turbulence is studied by means of direct numerical simulations. Due to anisotropy of the flow, horizontal and vertical dispersion show different behavior. Single-particle dispersion in horizontal direction is similar to that in isotropic turbulence for short times, but shows a long-time growth rate proportional to t2.1±0.1, larger than the classical linear diffusion limit. In vertical direction, three successive regimes can be identified: a classical t2-regime, a plateau that scales as N−2, and a diffusion limit where dispersion is proportional to t. By forcing the flow and performing long-time simulations, we are able to observe this last regime, which was predicted but not observed before in stratified turbulence. This diffusive regime is caused by molecular diffusion of the active scalar (density). The mean squared separation of particle pairs (relative dispersion) in vertical direction shows two plateaus that are not present in isotropic turbulence. They can be associated with the characteristic layered structure of the flow. In the long-time limit again a linear regime is found as for single-particle dispersion. Pair dispersion in horizontal direction behaves similar to that in isotropic turbulence except for long times. Finally, the study of multiparticle statistics in stably stratified turbulent flows is reported. The evolution of tetrads gives an impression of the shape of particle clouds. It is found that with increasing stratification, the volume of the tetrads decreases, and they become flatter and more elongated.

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Section: Introductionsupporting

confidence: 73%

Single-particle, particle-pair, and multiparticle dispersion of fluid particles in forced stably stratified turbulence

2008

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“…(Nicolleau & Vassilicos, 2000) was one of the first attempts to extend KS to stably stratified flows. These authors implemented the time evolution predicted by Rapid Distortion Theory (RDT)'s solution of the Boussinesq equation with the KS 3-D velocity field formalism.…”

Section: Introductionmentioning

confidence: 99%

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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“…Analytical results are derived using linear theory for the Eulerian velocity correlations (single-point, twotime) in the vertical and the horizontal directions, and Lagrangian ones are assumed to be equivalent, in agreement with an additional Corrsin assumption used by Kaneda (2000). They are compared with results from the kinematic simulation model (KS) by Nicolleau & Vassilicos (2000), which also incorporates the wave-vortex dynamics inherited from linear theory, and directly yields Lagrangian correlations as well as Eulerian ones. Finally, results from direct numerical simulations (DNS) are obtained and compared for the rotation-dominant case B =2Ω/N = 10, the stratificationdominant case B =1/10, the non-dispersive case B =1, and pure stratification B =0 and pure rotation N =0.…”

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confidence: 96%

Turbulent diffusion in rapidly rotating flows with and without stable stratification

et al. 2004

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In this work, three different approaches are used for evaluating some Lagrangian properties of homogeneous turbulence containing anisotropy due to the application of a stable stratification and a solid-body rotation. The two external frequencies are the magnitude of the system vorticity 2Ω,chosen vertical here, and the Brunt-Väisälä frequency N,w h i c hg i ves the strength of the vertical stratification. Analytical results are derived using linear theory for the Eulerian velocity correlations (single-point, twotime) in the vertical and the horizontal directions, and Lagrangian ones are assumed to be equivalent, in agreement with an additional Corrsin assumption used by Kaneda (2000). They are compared with results from the kinematic simulation model (KS) by Nicolleau & Vassilicos (2000), which also incorporates the wave-vortex dynamics inherited from linear theory, and directly yields Lagrangian correlations as well as Eulerian ones. Finally, results from direct numerical simulations (DNS) are obtained and compared for the rotation-dominant case B =2Ω/N = 10, the stratificationdominant case B =1/10, the non-dispersive case B =1, and pure stratification B =0 and pure rotation N =0. The last situation is shown to be singular with respect to the mixed stratified/rotating ones. We address the question of the validity of Corrsin's simplified hypothesis, which states the equivalence between Eulerian and Lagrangian correlations. Vertical correlations are found to follow this postulate, but not the horizontal ones. Consequences for the vertical and horizontal one-particle dispersion are examined. In the analytical model, the squared excursion lengths are calculated by time integrating the Lagrangian (equal to the Eulerian) two-time correlations, according to Taylor's procedure. These quantities are directly computed from fluctuating trajectories by both KS and DNS. In the case of pure rotation, the analytical procedure allows us to relate Brownian t-asymptotic laws of dispersion in both the horizontal and vertical directions to the angular phase-mixing properties of the inertial waves. If stratification is present, the inertia-gravity wave dynamics, which affects the vertical motion, yields a suppressed vertical diffusivity, but not a suppressed horizontal diffusivity, since part of the horizontal velocity field escapes wavy motion.

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Turbulent diffusion in stably stratified non-decaying turbulence

Cited by 39 publications

References 19 publications

Single-particle, particle-pair, and multiparticle dispersion of fluid particles in forced stably stratified turbulence

Single-particle, particle-pair, and multiparticle dispersion of fluid particles in forced stably stratified turbulence

Kinematic simulation for stably stratified and rotating turbulence

Turbulent diffusion in rapidly rotating flows with and without stable stratification

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