Open accessPosted Content

# Scaling turbulence in the near-wall region

Abstract: A new velocity scale is derived that yields a Reynolds number independent profile for the streamwise turbulent fluctuations in the near-wall region of wall bounded flows for $y^+<25$. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence distribution.

Topics: Turbulence (58%), Reynolds number (57%), Shear stress (50%)
##### Citations
More

5 results found

Open accessJournal Article
Abstract: A new scaling is derived that yields a Reynolds-number-independent profile for all components of the Reynolds stress in the near-wall region of wall-bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behaviour.

Topics: Boundary layer (61%), Reynolds stress (61%), Reynolds number (59%) ... show more

3 Citations

Open accessPosted Content
Abstract: The scaling of different features of stream-wise normal stress profiles $\langle uu\rangle^+(y^+)$ in turbulent wall-bounded flows, in particular in truly parallel flows, such as channel and pipe flows, is the subject of a long running debate. Particular points of contention are the scaling of the "inner" and "outer" peaks of $\langle uu\rangle^+$ at $y^+\approxeq 15$ and $y^+ =\mathcal{O}(10^3)$, respectively, their infinite Reynolds number limit, and the rate of logarithmic decay in the outer part of the flow. Inspired by the landmark paper of Chen and Sreenivasan (2021), two terms of the inner asymptotic expansion of $\langle uu\rangle^+$ in the small parameter $Re_\tau^{-1/4}$ are extracted for the first time from a set of direct numerical simulations (DNS) of channel flow. This inner expansion is completed by a matching outer expansion, which not only fits the same set of channel DNS within 1.5\% of the peak stress, but also provides a good match of laboratory data in pipes and the near-wall part of boundary layers, up to the highest $Re_\tau$'s of order $10^5$. The salient features of the new composite expansion are first, an inner $\langle uu\rangle^+$ peak, which saturates at 11.3 and decreases as $Re_\tau^{-1/4}$, followed by a short "wall loglaw" with a slope that becomes positive for $Re_\tau \gtrapprox 20'000$, leading up to an outer peak, and an outer logarithmic overlap with a negative slope continuously going to zero for $Re_\tau \to\infty$.

Topics: Order (ring theory) (50%)

3 Citations

Open accessPosted Content
Abstract: A new scaling is derived that yields a Reynolds number independent profile for all components of the Reynolds stress in the near-wall region of wall bounded flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behavior.

Topics: Reynolds stress (63%), Reynolds number (61%), Turbulence (59%) ... show more

2 Citations

Open accessJournal Article
Abstract: A new scaling is derived that yields a Reynolds number independent profile for all components of the Reynolds stress in the near-wall region of wall bounded flows, including channel, pipe and boundary layer flows. The scaling demonstrates the important role played by the wall shear stress fluctuations and how the large eddies determine the Reynolds number dependence of the near-wall turbulence behavior.

Topics: Boundary layer (61%), Reynolds stress (61%), Reynolds number (60%) ... show more

2 Citations

##### References
More

13 results found

Journal Article
M. V. Zagarola1, Alexander Smits1Institutions (1)
Abstract: Measurements of the mean velocity profile and pressure drop were performed in a fully developed, smooth pipe flow for Reynolds numbers from 31×103 to 35×106. Analysis of the mean velocity profiles indicates two overlap regions: a power law for 60 9×103). Von Karman's constant was shown to be 0.436 which is consistent with the friction factor data and the mean velocity profiles for 600 5%) than those predicted by Prandtl's relation. A new friction factor relation is proposed which is within ±1.2% of the data for Reynolds numbers between 10×103 and 35×106, and includes a term to account for the near-wall velocity profile.

Topics: Reynolds number (62%), Turbulence (62%), Shear velocity (61%) ... show more

760 Citations

Journal Article
David B. De Graaff1, John K. Eaton1Institutions (1)
Abstract: Despite extensive study, there remain significant questions about the Reynolds-number scaling of the zero-pressure-gradient flat-plate turbulent boundary layer. While the mean flow is generally accepted to follow the law of the wall, there is little consensus about the scaling of the Reynolds normal stresses, except that there are Reynolds-number effects even very close to the wall. Using a low-speed, high-Reynolds-number facility and a high-resolution laser-Doppler anemometer, we have measured Reynolds stresses for a flat-plate turbulent boundary layer from Reθ = 1430 to 31 000. Profiles of u′2, v′2, and u′v′ show reasonably good collapse with Reynolds number: u′2 in a new scaling, and v′2 and u′v′ in classic inner scaling. The log law provides a reasonably accurate universal profile for the mean velocity in the inner region.

750 Citations

Journal Article
Myoungkyu Lee1, Robert D. Moser1Institutions (1)
Abstract: A direct numerical simulation of incompressible channel flow at a friction Reynolds number ( ) of 5186 has been performed, and the flow exhibits a number of the characteristics of high-Reynolds-number wall-bounded turbulent flows. For example, a region where the mean velocity has a logarithmic variation is observed, with von Karman constant . There is also a logarithmic dependence of the variance of the spanwise velocity component, though not the streamwise component. A distinct separation of scales exists between the large outer-layer structures and small inner-layer structures. At intermediate distances from the wall, the one-dimensional spectrum of the streamwise velocity fluctuation in both the streamwise and spanwise directions exhibits dependence over a short range in wavenumber . Further, consistent with previous experimental observations, when these spectra are multiplied by (premultiplied spectra), they have a bimodal structure with local peaks located at wavenumbers on either side of the range.

714 Citations

Open accessJournal Article
Abstract: 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 at very large ones.

Topics: Reynolds number (58%), Turbulence (57%), Scaling (51%)

663 Citations

Journal Article
09 Jul 2010-Science
Abstract: The behavior of turbulent fluid motion, particularly in the thin chaotic fluid layers immediately adjacent to solid boundaries, can be difficult to understand or predict. These layers account for up to 50% of the aerodynamic drag on modern airliners and occupy the first 100 meters or so of the atmosphere, thus governing wider meteorological phenomena. The physics of these layers is such that the most important processes occur very close to the solid boundary—the region where accurate measurements and simulations are most challenging. We propose a mathematical model to predict the near-wall turbulence given only large-scale information from the outer boundary layer region. This predictive capability may enable new strategies for the control of turbulence and may provide a basis for improved engineering and weather prediction simulations.