Reynolds-number scaling of the flat-plate turbulent boundary layer

Graaff, David B. De; Eaton, John K.

doi:10.1017/s0022112000001713

Cited by 686 publications

(568 citation statements)

References 31 publications

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“…Figure 5(d) applies this scaling to the present simulations and to the measurements of de Graaff & Eaton (2000), Perry & Abell (1975) and Comte-Bellot (1965) . For such high Reynolds numbers, the one-dimensional spectrum would show a 'discontinuity' between (3.2) and (3.3) around λ x ≈ λ zc , marking the wavelength beyond which the structures cross the relatively sharp velocity drop near the wall.…”

Section: Spectra Of Turbulence In Channels 139supporting

confidence: 52%

“…The resulting spectral model can be integrated to obtain a mixed scaling for the total intensity of the fluctuating velocity, which collapses the numerical results well with those of de Graaff & Eaton (2000) in the outer layer, and which predicts that this part of the flow will tend to scale with the mean-stream velocity at very high Reynolds numbers. These results do not extend to the near-wall region.…”

Section: Discussionmentioning

confidence: 57%

“…That effect cannot necessarily be neglected, since the fractions , L950; ᭺, S550; ᮀ, S950; ᭝, S1900. The shaded region in (b) covers the maximum scatter of experimental boundary layers from Smith (1994), Re θ = 4600-13000, Österlund et al (2000), Re θ = 2500-27000, and de Graaff & Eaton (2000), Re θ = 1430-31000. The hatched area covers experimental pipes from Perry et al (1986), Re τ = 1600-3800, Durst et al (1995), Re τ = 271-570 and Zagarola & Smits (1997), Re τ = 1700-5.3 × 10 5 .…”

Section: The Numerical Experimentsmentioning

confidence: 99%

“…The discovery by de Graaff & Eaton (2000) that they scale well in mixed units was however unexpected, and presents a clear theoretical challenge, because it implies that they should be describable by a well-defined model.…”

Section: Introductionmentioning

confidence: 99%

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Scaling of the energy spectra of turbulent channels

et al. 2004

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The spectra and correlations of the velocity fluctuations in turbulent channels, especially above the buffer layer, are analysed using new direct numerical simulations with friction Reynolds numbers up to Re$_{\tau}\,{=}\,1900$. It is found, and explained, that their scaling is anomalous in several respects, including a square-root behaviour of their width with respect to their length, and a velocity scaling of the largest modes with the centreline velocity $U_c$. It is shown that this implies a logarithmic correction to the $k^{-1}$ energy spectrum, and that it leads to a scaling of the total fluctuation intensities away from the wall which agrees well with the mixed scaling of de Graaff & Eaton (2000) at intermediate Reynolds numbers, but which tends to a pure scaling with $U_c$ at very large ones.

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Section: Spectra Of Turbulence In Channels 139supporting

confidence: 52%

Section: Discussionmentioning

confidence: 57%

Section: The Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Scaling of the energy spectra of turbulent channels

et al. 2004

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“…The figure also displays the segments used to average the statistics of the three reference sections used later in the paper, listed in Erm & Joubert (1991), Reg = 1450 for the present simulation, Reg = 1430 for de Graaff & Eaton (2000), and Reg = 1410 for Schlatter et al (2009).…”

Section: Basic Statisticsmentioning

confidence: 99%

Turbulent boundary layers and channels at moderate Reynolds numbers

et al. 2010

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The behaviour of the velocity and pressure fluctuations in the outer layers of wall-bounded turbulent flows is analysed by comparing a new simulation of the zero-pressure-gradient boundary layer with older simulations of channels. The 99 % boundary-layer thickness is used as a reasonable analogue of the channel half-width, but the two flows are found to be too different for the analogy to be complete. In agreement with previous results, it is found that the fluctuations of the transverse velocities and of the pressure are stronger in the boundary layer, and this is traced to the pressure fluctuations induced in the outer intermittent layer by the differences between the potential and rotational flow regions. The same effect is also shown to be responsible for the stronger wake component of the mean velocity profile in external flows, whose increased energy production is the ultimate reason for the stronger fluctuations. Contrary to some previous results by our group, and by others, the streamwise velocity fluctuations are also found to be higher in boundary layers, although the effect is weaker. Within the limitations of the non-parallel nature of the boundary layer, the wall-parallel scales of all the fluctuations are similar in both the flows, suggesting that the scale-selection mechanism resides just below the intermittent region, y/S =0.3-0.5. This is also the location of the largest differences in the intensities, although the limited Reynolds number of the boundary-layer simulation (Reg «2000) prevents firm conclusions on the scaling of this location. The statistics of the new boundary layer are available from http://torroja.dmt.upm.es/ftp/blayers/.

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Turbulence Closure Models for Computational Fluid Dynamics

Durbin¹

2004

Encyclopedia of Computational Mechanics

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The formulation of analytical turbulence closure models for use in computational fluid mechanics is described. The subject of this chapter is the types of models that are used to predict the statistically averaged flow field-commonly known as Reynolds-averaged Navier-Stokes equations (RANS) modeling. A variety of models are reviewed: these include two-equation, eddy viscosity transport, and second moment closures. How they are formulated is not the main theme; it enters the discussion but the models are presented largely at an operational level. Several issues related to numerical implementation are discussed. Relative merits of the various formulations are commented on.

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Reynolds-number scaling of the flat-plate turbulent boundary layer

Cited by 686 publications

References 31 publications

Scaling of the energy spectra of turbulent channels

Scaling of the energy spectra of turbulent channels

Turbulent boundary layers and channels at moderate Reynolds numbers

Turbulence Closure Models for Computational Fluid Dynamics

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