Turbulent fluctuations above the buffer layer of wall-bounded flows
TL;DR: In this paper, the velocity and pressure fluctuations in the logarithmic and outer layers of turbulent flows are analyzed using spectral information and probability density functions from channel simulations at Reτ 2000.
Abstract: The behaviour of the velocity and pressure fluctuations in the logarithmic and outer layers of turbulent flows is analysed using spectral information and probability density functions from channel simulations at Reτ 2000. Comparisons are made with experimental data at higher Reynolds numbers. It is found, in agreement with previous investigations, that the intensity profiles of the streamwise and spanwise velocity components have logarithmic ranges that are traced to the widening spectral range of scales as the wall is approached. The same is true for the pressure, both theoretically and observationally, but not for the normal velocity or for the tangential stress cospectrum, although even those two quantities have structures with lengths of the order of several hundred times the wall distance. Because the logarithmic range grows longer as the Reynolds number increases, variables which are ‘attached’ in this sense scale in the buffer layer in mixed units. These results give strong support to the attached-eddy scenario proposed by Townsend (1976), but they are not linked to any particular eddy model. The scaling of the outer modes is also examined. The intensity of the streamwise velocity at fixed y/h increases with the Reynolds number. This is traced to the large-scale modes, and to an increased intensity of the ejections but not of the sweeps. Several differences are found between the outer structures of different flows. The outer modes of the spanwise and wall-normal velocities in boundary layers are stronger than in internal flows, and their streamwise velocities penetrate closer to the wall. As a consequence, their logarithmic layers are thinner, and some of their logarithmic slopes are different. The channel statistics are available electronically at http://torroja.dmt.upm.es/ftp/channels/.
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TL;DR: The Structure of Turbulent Shear Flow by Dr. A.Townsend as mentioned in this paper is a well-known work in the field of fluid dynamics and has been used extensively in many applications.
Abstract: The Structure of Turbulent Shear Flow By Dr. A. A. Townsend. Pp. xii + 315. 8¾ in. × 5½ in. (Cambridge: At the University Press.) 40s.
1,050 citations
TL;DR: In this article, the authors review wall-bounded turbulent flows, particularly high-Reynolds number, zero-pressure gradient boundary layers, and fully developed pipe and channel flows.
Abstract: We review wall-bounded turbulent flows, particularly high–Reynolds number, zero–pressure gradient boundary layers, and fully developed pipe and channel flows. It is apparent that the approach to an asymptotically high–Reynolds number state is slow, but at a sufficiently high Reynolds number the log law remains a fundamental part of the mean flow description. With regard to the coherent motions, very-large-scale motions or superstructures exist at all Reynolds numbers, but they become increasingly important with Reynolds number in terms of their energy content and their interaction with the smaller scales near the wall. There is accumulating evidence that certain features are flow specific, such as the constants in the log law and the behavior of the very large scales and their interaction with the large scales (consisting of vortex packets). Moreover, the refined attached-eddy hypothesis continues to provide an important theoretical framework for the structure of wall-bounded turbulent flows.
821 citations
Cites methods from "Turbulent fluctuations above the bu..."
...Recent surveys of the available data by Jiménez & Hoyas (2008) and Buschmann et al. (2009), together with analysis of DNS data by del Álamo & Jiménez (2003), del Álamo et al. (2004), and Hoyas & Jiménez (2006), provide support for the Townsend attached-eddy hypothesis predictions for v and w,…...
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TL;DR: In this paper, the authors distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy, and highlight some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters, and the scaling of mean flow and Reynolds stresses.
Abstract: Wall-bounded turbulent flows at high Reynolds numbers have become an increasingly active area of research in recent years. Many challenges remain in theory, scaling, physical understanding, experimental techniques, and numerical simulations. In this paper we distill the salient advances of recent origin, particularly those that challenge textbook orthodoxy. Some of the outstanding questions, such as the extent of the logarithmic overlap layer, the universality or otherwise of the principal model parameters such as the von Karman “constant,” the parametrization of roughness effects, and the scaling of mean flow and Reynolds stresses, are highlighted. Research avenues that may provide answers to these questions, notably the improvement of measuring techniques and the construction of new facilities, are identified. We also highlight aspects where differences of opinion persist, with the expectation that this discussion might mark the beginning of their resolution.
716 citations
TL;DR: In this paper, the authors analyse recent experimental data in the Reynolds number range of nominally 2 × 104 < Reτ < 6 × 105 for boundary layers, pipe flow and the atmospheric surface layer, and show that the data support the existence of a universal logarithmic region.
Abstract: Considerable discussion over the past few years has been devoted to the question of whether the logarithmic region in wall turbulence is indeed universal. Here, we analyse recent experimental data in the Reynolds number range of nominally 2 × 104 < Reτ < 6 × 105 for boundary layers, pipe flow and the atmospheric surface layer, and show that, within experimental uncertainty, the data support the existence of a universal logarithmic region. The results support the theory of Townsend (The Structure of Turbulent Shear Flow, Vol. 2, 1976) where, in the interior part of the inertial region, both the mean velocities and streamwise turbulence intensities follow logarithmic functions of distance from the wall. © 2013 Cambridge University Press.
618 citations
Cites result from "Turbulent fluctuations above the bu..."
...Tentative support has also come from other studies, notably Jiménez & Hoyas (2008)....
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TL;DR: In contrast to inferring model parameters, this work uses inverse modeling to obtain corrective, spatially distributed functional terms, offering a route to directly address model-form errors.
430 citations
References
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Book•
01 Jan 1955
TL;DR: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part, denoted as turbulence as discussed by the authors, and the actual flow is very different from that of the Poiseuille flow.
Abstract: The flow laws of the actual flows at high Reynolds numbers differ considerably from those of the laminar flows treated in the preceding part. These actual flows show a special characteristic, denoted as turbulence. The character of a turbulent flow is most easily understood the case of the pipe flow. Consider the flow through a straight pipe of circular cross section and with a smooth wall. For laminar flow each fluid particle moves with uniform velocity along a rectilinear path. Because of viscosity, the velocity of the particles near the wall is smaller than that of the particles at the center. i% order to maintain the motion, a pressure decrease is required which, for laminar flow, is proportional to the first power of the mean flow velocity. Actually, however, one ob~erves that, for larger Reynolds numbers, the pressure drop increases almost with the square of the velocity and is very much larger then that given by the Hagen Poiseuille law. One may conclude that the actual flow is very different from that of the Poiseuille flow.
17,321 citations
Journal Article•
TL;DR: In this article, the authors consider the problem of finding the components of the velocity at every point of a point with rectangular cartesian coordinates x 1, x 2, x 3, x 4, x 5, x 6, x 7, x 8.
Abstract: §1. We shall denote by uα ( P ) = uα ( x 1, x 2, x 3, t ), α = 1, 2, 3, the components of velocity at the moment t at the point with rectangular cartesian coordinates x 1, x 2, x 3. In considering the turbulence it is natural to assume the components of the velocity uα ( P ) at every point P = ( x 1, x 2, x 3, t ) of the considered domain G of the four-dimensional space ( x 1, x 2, x 3, t ) are random variables in the sense of the theory of probabilities (cf. for this approach to the problem Millionshtchikov (1939) Denoting by Ᾱ the mathematical expectation of the random variable A we suppose that ῡ 2 α and (d uα /d xβ )2― are finite and bounded in every bounded subdomain of the domain G .
6,063 citations
"Turbulent fluctuations above the bu..." refers background in this paper
...They tend to be roughly isotropic and to form classical Kolmogorov (1941) energy cascades....
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TL;DR: In this article, a direct numerical simulation of a turbulent channel flow is performed, where the unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points.
Abstract: A direct numerical simulation of a turbulent channel flow is performed. The unsteady Navier-Stokes equations are solved numerically at a Reynolds number of 3300, based on the mean centerline velocity and channel half-width, with about 4 million grid points. All essential turbulence scales are resolved on the computational grid and no subgrid model is used. A large number of turbulence statistics are computed and compared with the existing experimental data at comparable Reynolds numbers. Agreements as well as discrepancies are discussed in detail. Particular attention is given to the behavior of turbulence correlations near the wall. A number of statistical correlations which are complementary to the existing experimental data are reported for the first time.
4,788 citations
Additional excerpts
...1986; Perry & Li 1990; Kunkel & Marusic 2006). It is weaker than that for a uniform velocity scale. The idea is that all eddies are active somewhere, so that the only attached eddies are the maximal detached ones. At a given wall distance, eddies with wall-parallel sizes λ y are wall-parallel sections of larger eddies whose active central parts are located at yλ =O(λ). They are only inactive where their wall-normal velocities are blocked by the wall, y yλ. Their velocities away from the wall therefore scale with uτ , and their wall-parallel components presumably retain the same scaling. The energy in the spectral band yλ/2 λ<yλ is then O(u(2)τ ), and since such eddies exist for all y < yλ = O(λ) < h, integration of the spectrum between those limits results in a squared intensity proportional to log(h/y). This still implies that the velocity scale for the fluctuations at a fixed y/h is uτ , but when such inactive variables are measured at a fixed y, where y/h = Reτ −1y+, their squared intensities should be proportional u(2)τ log Reτ . For example, that should be true in the buffer layer. The last conclusion has been tested by several groups over the last decade. Convincing evidence that u′ increases in the buffer layer with the Reynolds number was first provided by DeGraaff & Eaton (2000). They proposed for u′2 an empirical ‘mixed’ scaling with uτUc, where Uc is the free-stream velocity....
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Book•
19 Dec 1975
TL;DR: In this paper, the authors present a method to find the optimal set of words for a given sentence in a sentence using the Bibliogr. Index Reference Record created on 2004-09-07, modified on 2016-08-08
Abstract: Note: Bibliogr. : p. 413-424. Index Reference Record created on 2004-09-07, modified on 2016-08-08
3,758 citations
TL;DR: In this paper, the turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub tta = 1410.
Abstract: The turbulent boundary layer on a flat plate, with zero pressure gradient, is simulated numerically at four stations between R sub theta = 225 and R sub theta = 1410. The three-dimensional time-dependent Navier-Stokes equations are solved using a spectra method with up to about 10 to the 7th power grid points. Periodic spanwise and stream-wise conditions are applied, and a multiple-scale procedure is applied to approximate the slow streamwise growth of the boundary layer. The flow is studied, primarily, from a statistical point of view. The solutions are compared with experimental results. The scaling of the mean and turbulent quantities with Reynolds number is examined and compared with accepted laws, and the significant deviations are documented. The turbulence at the highest Reynolds number is studied in detail. The spectra are compared with various theoretical models. Reynolds-stress budget data are provided for turbulence-model testing.
1,934 citations
"Turbulent fluctuations above the bu..." refers result in this paper
...The same is true for the highest Reynolds number in the boundary layer simulations of Spalart (1988), whose Reτ is comparable to that of case L550....
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