The return to isotropy of homogeneous turbulence

Choi, Kwing-So; Lumley, John L.

doi:10.1017/s002211200100386x

Cited by 236 publications

(166 citation statements)

References 9 publications

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“…Choi & Lumley 2001) . In particular, the ratio C 2 /C 1 is only weakly constrained through a comparison with Wendt's (1933) data, with a wide plausible range of roughly 0.4 to 1.…”

Section: Discussionmentioning

confidence: 99%

“…In fact, the limitations of the three-parameter model mean that no choice of the parameters can accurately match all experimental results. For example, Choi & Lumley (2001) find that the return to isotropy of homogeneous turbulence is more complicated than is assumed in any available closure model. In Section 4.2 below we compare the predictions of our model with data from Couette-Taylor experiments, and tentatively deduce an approximate value of C 2 ≃ 0.6.…”

Section: Comparison With Other Modelsmentioning

confidence: 99%

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A model for the nonlinear dynamics of turbulent shear flows

Garaud

Ogilvie

2005

J. Fluid Mech.

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We investigate the nonlinear dynamics of turbulent shear flows, with and without rotation, in the context of a simple but physically motivated closure of the equation governing the evolution of the Reynolds stress tensor. We show that the model naturally accounts for some familiar phenomena in parallel shear flows, such as the subcritical transition to turbulence at a finite Reynolds number and the occurrence of a universal velocity profile close to a wall at large Reynolds number. For rotating shear flows we find that, depending on the Rayleigh discriminant of the system, the model predicts either linear instability or nonlinear instability or complete stability as the Reynolds number is increased to large values. We investigate the properties of Couette-Taylor flows for varying inner and outer cylinder rotation rates and identify the region of linear instability (similar to Taylor's), as well as regions of finite-amplitude instability qualitatively compatible with recent experiments. We also discuss quantitative predictions of the model in comparison with a range of experimental torque measurements. Finally, we consider the relevance of this work to the question of the hydrodynamic stability of astrophysical accretion discs.

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“…Choi & Lumley 2001) . In particular, the ratio C 2 /C 1 is only weakly constrained through a comparison with Wendt's (1933) data, with a wide plausible range of roughly 0.4 to 1.…”

Section: Discussionmentioning

confidence: 99%

Section: Comparison With Other Modelsmentioning

confidence: 99%

A model for the nonlinear dynamics of turbulent shear flows

Garaud

Ogilvie

2005

J. Fluid Mech.

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“…The Rotta model has been the subject of numerous studies [35], and despite its limitations, remains widely employed in modeling pressurescalar interactions in high Reynolds number turbulent flows. The co-spectral nonlinear turbulent flux transport term was shown elsewhere to act mainly to transport covariance away from the peak in the co-spectra [30] (i.e.…”

Section: B a Simplified Co-spectral Budgetmentioning

confidence: 99%

Mean scalar concentration profile in a sheared and thermally stratified atmospheric surface layer

Katul

Chameki

et al. 2013

Phys. Rev. E

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Using only dimensional considerations, Monin and Obukhov proposed a 'universal' stability correction function φc(ζ) that accounts for distortions caused by thermal stratification to the mean scalar concentration profile in the atmospheric surface layer when the flow is stationary, planar homogeneous, fully turbulent, and lacking any subsidence. For nearly six decades, their analysis provided the basic framework for almost all operational models and data interpretation in the lower atmosphere. However, the canonical shape of φc(ζ) and the departure from the Reynold's analogy continue to defy theoretical explanation. Here, the basic processes governing the scalar-velocity cospectrum, including buoyancy and the scaling laws describing the velocity and temperature spectra, are considered via a simplified co-spectral budget. The solution to this co-spectral budget is then used to derive φc(ζ), thereby establishing a link between the energetics of turbulent velocity and scalar concentration fluctuations and the bulk flow describing the mean scalar concentration profile. The resulting theory explains all the canonical features of φc(ζ), including the onset of power-laws for various stability regimes and their concomitant exponents, as well as the causes of departure from Reynold's analogy.

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“…The second and third mathematical invariants of the normalized Reynolds stress anisotropy tensor together describe the possible states of realizable turbulence, represented with the anisotropy invariant map, referred to as an AIM, or Lumley's triangle [10]. Theoretical development of the anisotropic state of turbulence has further been employed in predictive models of turbulence often seen in the form of boundary conditions, as for wall-bounded turbulence.…”

Section: Introductionmentioning

confidence: 99%

Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

2017

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Proper orthogonal decomposition (POD) is applied to distinct data sets in order to characterize the propagation of error arising from basis truncation in the description of turbulence. Experimental data from stereo particle image velocimetry measurements in a wind turbine array and direct numerical simulation data from a fully developed channel flow are used to illustrate dependence of the anisotropy tensor invariants as a function of POD modes used in low-order descriptions. In all cases, ensembles of snapshots illuminate a variety of anisotropic states of turbulence. In the near wake of a model wind turbine, the turbulence field reflects the periodic interaction between the incoming flow and rotor blade. The far wake of the wind turbine is more homogenous, confirmed by the increased magnitude of the anisotropy factor. By contrast, the channel flow exhibits many anisotropic states of turbulence. In the inner layer of the wall-bounded region, one observes onecomponent turbulence at the wall; immediately above, the turbulence is dominated by two components, with the outer layer showing fully three-dimensional turbulence, conforming to theory for wall-bounded turbulence. The complexity of flow descriptions resulting from truncated POD bases can be greatly mitigated by severe basis truncations. However, the current work demonstrates that such simplification necessarily exaggerates the anisotropy of the modeled flow and, in extreme cases, can lead to the loss of three-dimensionality. Application of simple corrections to the low-order descriptions of the Reynolds stress tensor significantly reduces the residual root-mean-square error. Similar error reduction is seen in the anisotropy tensor invariants. Corrections of this form reintroduce three-dimensionality to severe truncations of POD bases. A threshold for truncating the POD basis based on the equivalent anisotropy factor for each measurement set required many more modes than a threshold based on energy. The mode requirement to reach the anisotropy threshold after correction is reduced by a full order of magnitude for all example data sets, ensuring that economical low-dimensional models account for the isotropic quality of the turbulence field.

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The return to isotropy of homogeneous turbulence

Cited by 236 publications

References 9 publications

A model for the nonlinear dynamics of turbulent shear flows

A model for the nonlinear dynamics of turbulent shear flows

Mean scalar concentration profile in a sheared and thermally stratified atmospheric surface layer

Anisotropic character of low-order turbulent flow descriptions through the proper orthogonal decomposition

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