Mean velocity and length-scales in the overlap region of wall-bounded turbulent flows

Mizuno, Yoshinori; Jiménez, Javier

doi:10.1063/1.3626406

Cited by 39 publications

(44 citation statements)

References 34 publications

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“…For example, by using an iterative curve-fitting procedure, Mizuno & Jimenez (2011) demonstrate that for the δ + = 2004 flow of figure 7 their modified mixing length model exhibits its optimal behaviour over a domain that extends from ∼100 y + 1100. The present theoretical prediction indicates that the onset of the self-similarity associated with A(β) const.…”

Section: Discussionmentioning

confidence: 99%

“…Their analysis went up to δ + 8500 in the boundary layer and δ + 4000 in the channel. The offset appears in the formula of Mizuno & Jimenez (2011) owing to their use of a higher-order approximation. This is distinct from the overlap-layer-based arguments of Spalart et al (2008) and Wosnik et al (2000), which portray the offset as part of the leading-order equation.…”

Section: Elements Of the Channel And Pipe Flow Analysismentioning

confidence: 98%

“…From an analysis of their Ekman boundary layer DNS, Spalart, Coleman & Johnstone (2008) found that an offset of C = −7.5 yielded the largest extent of logarithmic-like dependence. Within the context of the overlap layer hypothesis, Mizuno & Jimenez (2011) utilized curve fits in concert with a mixing length model and found best-fitting values for C equal to −8.5 and 3.8 for channels and boundary layers, respectively. Their analysis went up to δ + 8500 in the boundary layer and δ + 4000 in the channel.…”

Section: Elements Of the Channel And Pipe Flow Analysismentioning

confidence: 99%

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Self-similar mean dynamics in turbulent wall flows

Klewicki

2013

J. Fluid Mech.

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This study investigates how and why dynamical self-similarities emerge with increasing Reynolds number within the canonical wall flows beyond the transitional regime. An overarching aim is to advance a mechanistically coherent description of turbulent wall-flow dynamics that is mathematically tractable and grounded in the mean dynamical equations. As revealed by the analysis of Fife, Klewicki & Wei (J. Discrete Continuous Dyn. Syst. A, vol. 24, 2009, pp. 781-807), the equations that respectively describe the mean dynamics of turbulent channel, pipe and boundary layer flows formally admit invariant forms. These expose an underlying self-similar structure. In all cases, two kinds of dynamical self-similarity are shown to exist on an internal domain that, for all Reynolds numbers, extends from O(ν/u τ ) to O(δ), where ν is the kinematic viscosity, u τ is the friction velocity and δ is the half-channel height, pipe radius, or boundary layer thickness. The simpler of the two self-similarities is operative on a large outer portion of the relevant domain. This self-similarity leads to an explicit analytical closure of the mean momentum equation. This self-similarity also underlies the emergence of a logarithmic mean velocity profile. A more complicated kind a self-similarity emerges asymptotically over a smaller domain closer to the wall. The simpler self-similarity allows the mean dynamical equation to be written as a closed system of nonlinear ordinary differential equations that, like the similarity solution for the laminar flat-plate boundary layer, can be numerically integrated. The resulting similarity solutions are demonstrated to exhibit nearly exact agreement with direct numerical simulations over the solution domain specified by the theory. At the Reynolds numbers investigated, the outer similarity solution is shown to be operative over a domain that encompasses ∼40 % of the overall width of the flow. Other properties predicted by the theory are also shown to be well supported by existing data.

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Section: Discussionmentioning

confidence: 99%

Section: Elements Of the Channel And Pipe Flow Analysismentioning

confidence: 98%

Section: Elements Of the Channel And Pipe Flow Analysismentioning

confidence: 99%

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Self-similar mean dynamics in turbulent wall flows

Klewicki

2013

J. Fluid Mech.

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“…The key in answering this question can be found from previous findings where the spanwise length scale of energy-containing motions in the logarithmic region is shown to be linearly proportional to the distance from the wall (Tomkins & Adrian 2003;delÁlamo et al 2004;Ganapathisubramani et al 2005;Hutchins et al 2005). We note that recent investigations have shown that the local mixing length scale defined by l(y) = u τ (dU/dy) −1 provides a better length scale for the logarithmic region (Mizuno & Jiménez 2011;Pirozzoli 2012), but this mixing length scale also gives the linear growth of the spanwise length scale at least at the leading-order, specially if the logarithmic behaviour becomes evident as for the flows at sufficiently high Reynolds numbers.…”

Section: Computing Attached Eddies At a Given Length Scalementioning

confidence: 94%

Statistical structure of self-sustaining attached eddies in turbulent channel flow

2015

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The linear growth of the spanwise correlation length scale with the distance from the wall in the logarithmic region of wall-bounded turbulent flows has been understood as a reflection of Townsend's attached eddies. Based on this observation, in the present study, we perform a numerical experiment, which simulates energy-containing motions only at a given spanwise length scale in the logarithmic region, using their self-sustaining nature found recently. The self-sustaining energy-containing motions at each of the spanwise length scales are found to be self-similar with respect to the given spanwise length. Furthermore, their statistical structures are consistent with those of the attached eddies given in the original theory, providing direct evidence on the existence of Townsend's attached eddies. It is shown that the single self-sustaining attached eddy is composed of two distinct elements, one of which is a long streaky motion reaching the near-wall region, and the other is a relatively short vortical structure carrying all the velocity components. For the given spanwise length λ z between λ + z = 100 and λ z ≃ 1.5h, the former is found to be self-similar along y ≃ 0.1λ z and λ x ≃ 10λ z , while the latter is self-similar along y ≃ 0.5 ∼ 0.7λ z and λ x ≃ 2 ∼ 3λ z . The scaling suggests that the smallest attached eddy would be a near-wall coherent motion given in the form of a streak and quasi-streamwise vortices aligned, whereas the largest one would be an outer motion with a very-largescale motion and large-scale motions aligned. The attached eddies in-between, the size of which is proportional to their distance from the wall, contribute to the logarithmic region and fill the space caused by the length scale separation. The scaling is also found to yield consistent behaviour with the emergence of k −1 x spectra in a number of previous studies. Finally, a further discussion is provided specially on the Townsend's inactive motion and several recent theoretical findings.

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“…A more conservative definition of the logarithmic layer, in terms of the mean velocity profile, only extends to y/h ≈ 0.15, especially in boundary layers (Nagib et al 2006), but that outer limit is mostly due to the relatively strong 'wake' component of the mean velocity profile in external flows, which is a consequence of the rotational-irrotational intermittency along the edge of the boundary layer ). The wake is much weaker in internal flows, and it was shown by Mizuno & Jiménez (2011) that the logarithmic fit of the mean profile can be extended in channels to y/h ≈ 0.5 by a simple modification of the classical law. Moreover, neither the logarithmic mean profile nor the linear spectral scaling will be particularly important in most of the following.…”

Section: The Numerical Experimentsmentioning

confidence: 99%

Simulations of turbulent channels with prescribed velocity profiles

Tuerke

Jiménez

2013

J. Fluid Mech.

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Direct numerical simulations of turbulent channels with artificially prescribed velocity profiles are discussed, using both natural and purposely incorrect profiles. It is found that turbulence develops correctly when natural profiles are prescribed, but that even slightly incorrect ones modify the Reynolds stresses substantially. That is used to study the dynamics of the energy-containing velocity fluctuations. The stronger (weaker) structures generated by locally stronger (weaker) mean shears have essentially correct isotropy coefficients but they are out of energy equilibrium, with the energy imbalance compensated by turbulent diffusion. The velocity scale in smooth profiles changes with the distance to the wall, and is best described by a friction velocity derived from the local total tangential stress. The behaviour across sharper shear jumps is more consistent with non-equilibrium eddies that relax over wall-normal distances of the order of the distance to the wall, suggesting that the energy equilibrium in the logarithmic layer is not local to a given height, but applies to extended layers homogenized by wall-normal fluxes. Examples of that non-local character are the large-scale inactive fluctuations near the wall, whose velocities do not scale with the local shear stress, but with that of their active 'cores' farther away from the wall.

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Mean velocity and length-scales in the overlap region of wall-bounded turbulent flows

Cited by 39 publications

References 34 publications

Self-similar mean dynamics in turbulent wall flows

Self-similar mean dynamics in turbulent wall flows

Statistical structure of self-sustaining attached eddies in turbulent channel flow

Simulations of turbulent channels with prescribed velocity profiles

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