Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003

Hoyas, Sergio; Jiménez, Javier

doi:10.1063/1.2162185

Cited by 896 publications

(932 citation statements)

References 12 publications

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“…The velocity profiles now in wall units and logarithmic y axis in figure 2(b) reveal a 'visual' log layer to y + of about 250 on the FPG side (where the shear stress has fallen by 14 %) and very close agreement with Poiseuille results by Hoyas & Jiménez (2006). Its approximate Kármán constant, simply using a ruler, is 0.42.…”

Section: General Presentationsupporting

confidence: 67%

“…Stimulated by two reviews, the p + conjecture is given a test at face value in figure 6, which shows U + at y + = 50 versus p + for a range of flows, from experiments and DNS (Spalart 1986;Nagano et al 1992;Spalart & Watmuff 1993;Volino & Simon 1997;Hoyas & Jiménez 2006;Spalart et al 2009;Wu & Moin 2008). The same test applied at y + = 1, limited to DNS, agrees very well with the viscous Taylor expansion ∂U + /∂p + = (1/2)y +2 , neglecting the Reynolds shear stress.…”

Section: Test Of the Scaling Lawsmentioning

confidence: 99%

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The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation

2009

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Wall-bounded turbulence in pressure gradients is studied using direct numerical simulation (DNS) of a Couette–Poiseuille flow. The motivation is to include adverse pressure gradients, to complement the favourable ones present in the well-studied Poiseuille flow, and the central question is how the scaling laws react to a gradient in the total shear stress or equivalently to a pressure gradient. In the case considered here, the ratio of local stress to wall stress, namely τ+, ranges from roughly 2/3 to 3/2 in the ‘wall region’. By this we mean the layer believed not to be influenced by the opposite wall and therefore open to simple, universal behaviour. The normalized pressure gradients p+ ≡ dτ+/dy+ at the two walls are −0.00057 and +0.0037. The outcome is in broad agreement with the findings of Galbraith, Sjolander & Head (Aeronaut. Quart. vol. 27, 1977, pp. 229–242) relating to boundary layers (based on measured profiles): the logarithmic velocity profile is much more resilient than two other, equally plausible assumptions, namely universality of the mixing length ℓ = κy and that of the eddy viscosity νt = uτκy. In pressure gradients, with τ+ ≠ 1, these three come into conflict, and our primary purpose is to compare them. We consider that the Kármán constant κ is unique but allow a range from 0.38 to 0.41, consistent with the current debates. It makes a minor difference in the interpretation. This finding of resilience appears new as a DNS result and is free of the experimental uncertainty over skin friction. It is not as distinct in the (rather strong) adverse gradient as it is in the favourable one; for instance the velocity U+ at y+ = 50 is lower by 3% on the adverse gradient side. A plausible cause is that the wall shear stress is small and somewhat overwhelmed by the stress and kinetic energy in the bulk of the flow. The potential of a correction to the ‘law of the wall’ based purely on p+ is examined, with mixed results. We view the preference for the log law as somewhat counter-intuitive in that the scaling law is non-local but also as becoming established and as highly relevant to turbulence modelling.

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Section: General Presentationsupporting

confidence: 67%

Section: Test Of the Scaling Lawsmentioning

confidence: 99%

The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation

2009

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“…The wall-normal velocity has a much shorter spectrum than any of the other components, lacking inactive motions (del Alamo et al 2004;Hoyas & Jiménez 2006). Its width is similar to that of either u or p at those short wavelengths, but the integrated spanwise spectra for any of those fluctuations are broadened by their wider components at longer wavelengths, which are missing for v.…”

Section: Spectramentioning

confidence: 96%

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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“…Throughout the paper, inner variables will be used and denoted with the superscript +, implying normalization of lengths with the friction length ν/u τ and velocities with the friction velocity u τ = √ τ w /ρ where τ w is the average shear stress at the wall. The computational domain is 8πh × 2h × 3πh and the resolution in the homogeneous directions is x + = 8.2 and z + = 4.1, see Hoyas & Jiménez (2006) for the details of the simulation. The velocity and pressure increments, δu i and δp respectively, appearing in the generalized Kolmogorov equation (2.1) are computed directly in physical space over the whole computational box by considering the values of velocity and pressure at the two points of the increment.…”

Section: Introductionmentioning

confidence: 99%

Cascades and wall-normal fluxes in turbulent channel flows

et al. 2016

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The present work describes the multidimensional behaviour of scale-energy production, transfer and dissipation in wall-bounded turbulent flows. This approach allows us to understand the cascade mechanisms by which scale energy is transmitted scale-by-scale among different regions of the flow. Two driving mechanisms are identified. A strong scale-energy source in the buffer layer related to the near-wall cycle and an outer scale-energy source associated with an outer turbulent cycle in the overlap layer. These two sourcing mechanisms lead to a complex redistribution of scale energy where spatially evolving reverse and forward cascades coexist. From a hierarchy of spanwise scales in the near-wall region generated through a reverse cascade and local turbulent generation processes, scale energy is transferred towards the bulk, flowing through the attached scales of motion, while among the detached scales it converges towards small scales, still ascending towards the channel centre. The attached scales of wall-bounded turbulence are then recognized to sustain a spatial reverse cascade process towards the bulk flow. On the other hand, the detached scales are involved in a direct forward cascade process that links the scale-energy excess at large attached scales with dissipation at the smaller scales of motion located further away from the wall. The unexpected behaviour of the fluxes and of the turbulent generation mechanisms may have strong repercussions on both theoretical and modelling approaches to wall turbulence. Indeed, actual turbulent flows are shown here to have a much richer physics with respect to the classical notion of turbulent cascade, where anisotropic production and inhomogeneous fluxes lead to a complex redistribution of energy where a spatial reverse cascade plays a central role.

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Scaling of the velocity fluctuations in turbulent channels up to Reτ=2003

Cited by 896 publications

References 12 publications

The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation

The resilience of the logarithmic law to pressure gradients: evidence from direct numerical simulation

Turbulent boundary layers and channels at moderate Reynolds numbers

Cascades and wall-normal fluxes in turbulent channel flows

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