Journal ArticleDOI
On the logarithmic mean profile
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TLDR
Wei et al. as discussed by the authors showed that the first principles of the NavierStokes equations admit a hierarchy of scaling layers, each having a distinct characteristic length, and that these characteristic lengths asymptotically scale with distance from the wall over a well-defined range of wall-normal positions.Abstract:
Elements of the first-principles-based theory of Wei et al. (J. Fluid Mech., vol. 522, 2005, p. 303), Fife et al. (Multiscale Model. Simul., vol. 4, 2005a, p. 936; J. Fluid Mech., vol. 532, 2005b, p. 165) and Fife, Klewicki & Wei (J. Discrete Continuous Dyn. Syst., vol. 24, 2009, p. 781) are clarified and their veracity tested relative to the properties of the logarithmic mean velocity profile. While the approach employed broadly reveals the mathematical structure admitted by the time averaged NavierStokes equations, results are primarily provided for fully developed pressure driven flow in a two-dimensional channel. The theory demonstrates that the appropriately simplified mean differential statement of Newton's second law formally admits a hierarchy of scaling layers, each having a distinct characteristic length. The theory also specifies that these characteristic lengths asymptotically scale with distance from the wall over a well-defined range of wall-normal positions, y. Numerical simulation data are shown to support these analytical findings in every measure explored. The mean velocity profile is shown to exhibit logarithmic dependence (exact or approximate) when the solution to the mean equation of motion exhibits (exact or approximate) self-similarity from layer to layer within the hierarchy. The condition of pure self-similarity corresponds to a constant leading coefficient in the logarithmic mean velocity equation. The theory predicts and clarifies why logarithmic behaviour is better approximated as the Reynolds number gets large. An exact equation for the leading coefficient (von Karman coefficient κ) is tested against direct numerical simulation (DNS) data. Two methods for precisely estimating the leading coefficient over any selected range of y are presented. These methods reveal that the differences between the theory and simulation are essentially within the uncertainty level of the simulation. The von Krmn coefficient physically exists owing to an approximate self-similarity in the flux of turbulent force across an internal layer hierarchy. Mathematically, this self-similarity relates to the slope and curvature of the Reynolds stress profile, or equivalently the slope and curvature of the mean vorticity profile. The theory addresses how, why and under what conditions logarithmic dependence is approximated relative to the specific mechanisms contained within the mean statement of dynamics. © 2009 Copyright Cambridge University Press.read more
Citations
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Boundary Layer Theory
TL;DR: The boundary layer equations for plane, incompressible, and steady flow are described in this paper, where the boundary layer equation for plane incompressibility is defined in terms of boundary layers.
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The Structure of Turbulent Shear Flow
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.
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High–Reynolds Number Wall Turbulence
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.
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On the logarithmic region in wall turbulence
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.
Journal ArticleDOI
Generalized logarithmic law for high-order moments in turbulent boundary layers
Charles Meneveau,Ivan Marusic +1 more
TL;DR: In this article, it was shown that the -order moments, raised to the power, also follow logarithmic behaviour according to, where is the velocity fluctuation normalized by the friction velocity, is an outer length scale and are non-universal constants.
References
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Book
Boundary layer theory
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.
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A First Course in Turbulence
Henk Tennekes,John L. Lumley +1 more
TL;DR: In this paper, the authors present a reference record created on 2005-11-18, modified on 2016-08-08 and used for the analysis of turbulence and transport in the context of energie.
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The Structure of Turbulent Shear Flow
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
MonographDOI
Turbulent Transport of Momentum and Heat
Henk Tennekes,John L. Lumley +1 more
TL;DR: In this article, the authors discuss the Reynolds equations and estimate of the Reynolds stress in the kinetic theory of gases, and describe the effects of shear flow near a rigid wall.