Probability density function of turbulent velocity fluctuations in a rough-wall boundary layer

Mouri, Hideaki; Takaoka, Masanori; Hori, Akihiro; Kawashima, Yoshihide

doi:10.1103/physreve.68.036311

Cited by 13 publications

(14 citation statements)

References 15 publications

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“…The sub-Gaussian results (with pdf flatness factor F =< u 4 > / < u 2 > less than 3) are probably from the dominance of a small number of large-scale modes, while the hyper-Gaussian results (F > 3) may be the result of correlations between Fourier modes Mouri et al 2003), an alignment of vortex tubes (Takaoka 1995), or intermittency (Schlichting & Gersten 2000). The results are unexplained quantitatively.…”

Section: Velocity Probability Distributionmentioning

confidence: 67%

“…This can be seen by noting that successive velocities are positively correlated for inelastic point particles conserving mass and momentum but not energy. Then the velocity changes are not independent and the central limit theorem does not apply (see Mouri et al 2003). Such correlations, resulting entirely from the large range of dissipation scales, would be a fundamental difference between incompressible and supersonic turbulence.…”

Section: Velocity Probability Distributionmentioning

confidence: 99%

“…Recent evidence for non-Gaussian velocity pdfs have been found for incompressible turbulence from experimental atmospheric data (Sreenivasan & Dhruva 1998), turbulent jets (Noullez et al 1997), boundary layers (Mouri et al 2003), and quasi-2D turbulence (Bracco et al 2000). The sub-Gaussian results (with pdf flatness factor F =< u 4 > / < u 2 > less than 3) are probably from the dominance of a small number of large-scale modes, while the hyper-Gaussian results (F > 3) may be the result of correlations between Fourier modes Mouri et al 2003), an alignment of vortex tubes (Takaoka 1995), or intermittency (Schlichting & Gersten 2000).…”

Section: Velocity Probability Distributionmentioning

confidence: 99%

See 2 more Smart Citations

Interstellar Turbulence I: Observations and Processes

Elmegreen

Scalo

2004

Annu. Rev. Astron. Astrophys.

1,125

983

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Turbulence affects the structure and motions of nearly all temperature and density regimes in the interstellar gas. This two-part review summarizes the observations, theory, and simulations of interstellar turbulence and their implications for many fields of astrophysics. The first part begins with diagnostics for turbulence that have been applied to the cool interstellar medium, and highlights their main results. The energy sources for interstellar turbulence are then summarized along with numerical estimates for their power input. Supernovae and superbubbles dominate the total power, but many other sources spanning a large range of scales, from swing amplified gravitational instabilities to cosmic ray streaming, all contribute in some way. Turbulence theory is considered in detail, including the basic fluid equations, solenoidal and compressible modes, global inviscid quadratic invariants, scaling arguments for the power spectrum, phenomenological models for the scaling of higher order structure functions, the direction and locality of energy transfer and cascade, velocity probability distributions, and turbulent pressure. We emphasize expected differences between incompressible and compressible turbulence. Theories of magnetic turbulence on scales smaller than the collision mean free path are included, as are theories of magnetohydrodynamic turbulence and their various proposals for power spectra. Numerical simulations of interstellar turbulence are reviewed. Models have reproduced the basic features of the observed scaling relations, predicted fast decay rates for supersonic MHD turbulence, and derived probability distribution functions for density. Thermal instabilities and thermal phases have a new interpretation in a supersonically turbulent medium. Large-scale models with various combinations of self-gravity, magnetic fields, supernovae, and -2 -star formation are beginning to resemble the observed interstellar medium in morphology and statistical properties. The role of self-gravity in turbulent gas evolution is clarified, leading to new paradigms for the formation of star clusters, the stellar mass function, the origin of stellar rotation and binary stars, and the effects of magnetic fields. The review ends with a reflection on the progress that has been made in our understanding of the interstellar medium, and offers a list of outstanding problems.

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Section: Velocity Probability Distributionmentioning

confidence: 67%

Section: Velocity Probability Distributionmentioning

confidence: 99%

Section: Velocity Probability Distributionmentioning

confidence: 99%

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Interstellar Turbulence I: Observations and Processes

Elmegreen

Scalo

2004

Annu. Rev. Astron. Astrophys.

1,125

983

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“…20 The log-law sublayer was at z Ӎ 0.15-0.35 m. The measurement was done at z = 0.25 and 0.70 m. The height z = 0.25 was in the log-law sublayer, where various eddies filled the space randomly and independently. 16 The flatness factor ͗v͑x͒ 4 ͘ / ͗v͑x͒ 2 ͘ 2 was close to the Gaussian value of 3. The height z = 0.70 m was in the wake sublayer, where eddies did not fill the space.…”

Section: A Experimentsmentioning

confidence: 89%

On Landau’s prediction for large-scale fluctuation of turbulence energy dissipation

et al. 2006

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Kolmogorov's theory for turbulence, proposed in 1941, is based on a hypothesis that small-scale statistics are uniquely determined by the kinematic viscosity and the mean rate of energy dissipation. Landau remarked that the local rate of energy dissipation should fluctuate in space over large scales and hence should affect small-scale statistics. Experimentally, we confirm the significance of this large-scale fluctuation, which is comparable to the mean rate of energy dissipation at the typical scale for energy-containing eddies. The significance is independent of the Reynolds number and the configuration for turbulence production. With an increase of scale r above the scale of largest energy-containing eddies, the fluctuation comes to have the scaling r −1/2 and becomes close to Gaussian. We also confirm that the large-scale fluctuation affects small-scale statistics.

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“…It ensures that the turbulence was fully developed and various eddies filled the space randomly and independently. 23,24 Not always close to the Gaussian value were u 3 / u 2 3/2 and u 4 / u 2 2 − 3 (Table I). They are sensitive to specific features of the energy-containing eddies that depend on the grid, the roughness, or the nozzle.…”

Section: Appendix: Details Of Experimentsmentioning

confidence: 99%

Statistical mechanics and large-scale velocity fluctuations of turbulence

et al. 2011

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Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are thereby analogous to thermal fluctuations studied in the statistical mechanics. By using this analogy, we describe the large-scale fluctuations of turbulence in a formalism that has the same mathematical structure as used for canonical ensembles in the statistical mechanics. The formalism yields a universal law for the energy distribution of the fluctuations, which is confirmed with experiments of a variety of turbulent flows. Thus, through the large-scale fluctuations, turbulence is related to the statistical mechanics.

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Probability density function of turbulent velocity fluctuations in a rough-wall boundary layer

Cited by 13 publications

References 15 publications

Interstellar Turbulence I: Observations and Processes

Interstellar Turbulence I: Observations and Processes

On Landau’s prediction for large-scale fluctuation of turbulence energy dissipation

Statistical mechanics and large-scale velocity fluctuations of turbulence

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