Velocity Defect Law

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W G Nickling - One of the best experts on this subject based on the ideXlab platform.

  • analysis of Velocity profile measurements from wind tunnel experiments with saltation
    Geomorphology, 2004
    Co-Authors: Bernard O Bauer, Chris Houser, W G Nickling
    Abstract:

    Abstract Investigations of wind-field modification due to the presence of saltating sediments have relied heavily on wind tunnels, which are known to impose geometric constraints on full boundary layer development. There remains great uncertainty as to which portion of the vertical wind-speed profile to analyze when deriving estimates of shear Velocity or surface roughness length because the lower sections are modified to varying degree by saltation, whereas the upper segments may be altered by artificially induced wake-like effects. Thus, it is not obvious which of several alternative Velocity-profile parameterizations (e.g., Law of the Wall, Velocity Defect Law, Wake Law) should be employed under such circumstances. A series of experimental wind-tunnel runs was conducted across a range of wind speed using fine- and coarse-grained sand to collect high-quality, fine-resolution data within and above the saltation layer using thermal anemometry and ruggedized probes. After each run, the rippled bottom was fixed with fine mist, and the experiment repeated without saltation. The measured wind-speed profiles were analyzed using six different approaches to derive estimates of shear Velocity and roughness length. The results were compared to parameter estimates derived directly from sediment transport rate measurements, and on this basis, it is suggested that one of the six approaches is more robust than the others. Specifically, the best estimate of shear Velocity during saltation is provided by the logarithmic Law applied to the profile data within about 0.05 m of the bottom, despite the fact that this near-surface region is where profile modification by saltating sediments is most pronounced. Uncertainty remains as to whether this conclusion can be generalized to field situations because progressive downwind adjustments in the interrelationship between the saltation layer and the wind field are anticipated in wind tunnels, thereby confounding most analyses based on equilibrium assumptions.

Mengjie Ding - One of the best experts on this subject based on the ideXlab platform.

  • Velocity Defect Laws log Law and logarithmic friction Law in the convective atmospheric boundary layer
    Journal of Fluid Mechanics, 2020
    Co-Authors: Chenning Tong, Mengjie Ding
    Abstract:

    The mean Velocity profile in the convective atmospheric boundary layer (CBL) is derived analytically. The shear-stress budget equations and the mean momentum equations are employed in the derivation. The multi-point Monin–Obukhov similarity (MMO) recently proposed and analytically derived by Tong & Nguyen (J. Atmos. Sci., vol. 72, 2015, pp. 4337–4348) and Tong & Ding (J. Fluid Mech., vol. 864, 2019, pp. 640–669) provides the scaling properties of the statistics in the shear-stress budget equations. Our previous and present studies have shown that the CBL is mathematically a singular perturbation problem. Therefore, we obtain the mean Velocity profile using the method of matched asymptotic expansions. Three scaling layers are identified: the outer layer, which includes the mixed layer, the inner-outer layer and the inner-inner layer, which includes the roughness layer. There are two overlapping layers, the local-free-convection layer and the log layer, respectively. Two new Velocity-Defect Laws are discovered: the mixed-layer Velocity-Defect Law and the surface-layer Velocity-Defect Law. The local-free-convection mean profile is obtained by asymptotically matching the expansions in the first two layers. The log Law is obtained by matching the expansions in the last two layers. The von Karman constant is obtained using Velocity and length scales, and therefore has a physical interpretation. A new friction Law, the convective logarithmic friction Law, is obtained. The present work provides an analytical derivation of the mean Velocity profile hypothesized in the Monin–Obukhov similarity theory, and is part of a comprehensive derivation of the MMO scaling from first principles.

Arne V Johansson - One of the best experts on this subject based on the ideXlab platform.

  • evaluation of scaling Laws derived from lie group symmetry methods in zero pressure gradient turbulent boundary layers
    Journal of Fluid Mechanics, 2004
    Co-Authors: Bjorn Lindgren, Jens M Osterlund, Arne V Johansson
    Abstract:

    New scaling Laws for turbulent boundary layers recently derived (see Oberlack 2000) using Lie group symmetry methods have been tested against experimental data from the KTH database for zero-pressure-gradient turbulent boundary layers. The most significant new Law predicts an exponential variation of the mean Velocity Defect in the outer (wake) region. It was shown to fit the experimental data very well over a large part of the boundary layer, from the outer part of the overlap region to about half the boundary layer thickness ( $\delta_{99}$ ). In the outermost part of the boundary layer the Velocity Defect falls more rapidly than predicted by the exponential Law. This can partly be attributed to intermittency in that region but the main cause stems from non-parallel effects that are not accounted for in the derivation of the exponential Law. The two-point correlation function behaviour in the outer region, where an exponential Velocity Defect Law is observed, was found to be very different from that derived under the assumption of parallel flow. It is found to be plausible that this indeed can be attributed to non-parallel effects. A small modification of the innermost part of the log-layer in the form of an additive constant within the log-function is predicted by the Lie group symmetry method. A qualitative agreement with such a behaviour just below the overlap region was found. The derived scaling Law behaviour in the overlap region for the two-point correlation functions was also verified by the experimental data.

Martin Oberlack - One of the best experts on this subject based on the ideXlab platform.

  • analytical study of turbulent poiseuille flow with wall transpiration
    Physics of Fluids, 2008
    Co-Authors: I I Vigdorovich, Martin Oberlack
    Abstract:

    An incompressible, pressure-driven, fully developed turbulent flow between two parallel walls, with an extra constant transverse Velocity component, is considered. A closure condition is formulated, which relates the shear stress to the first and the second derivatives of the longitudinal mean Velocity. The closure condition is derived without invoking any special hypotheses on the nature of turbulent motion, only taking advantage of the fact that the flow depends on a finite number of governing parameters. By virtue of the closure condition, the momentum equation is reduced to the boundary-value problem for a second-order differential equation, which is solved by the method of matched asymptotic expansions at high values of the logarithm of the Reynolds number based on the friction Velocity. There are three characteristic flow regions in the channel: the core region and two wall regions near injection and suction walls. For each region, the solution is constructed. The asymptotic matching gives formulas for the wall shear stress and the maximum mean Velocity. A limit transpiration Velocity is obtained, such that the shear stress at the injection wall vanishes, while the maximum point on the Velocity profile approaches the suction wall. In this case, a sublayer near the suction wall appears where the mean Velocity is proportional to the square root of the distance from the wall. A friction Law for Poiseuille flow with transpiration is found, which makes it possible to describe the relation between the wall shear stress, the Reynolds number, and the transpiration Velocity by a function of one variable. A Velocity Defect Law, which generalizes the classical Law for the core region in a channel with impermeable walls to the case of transpiration, is also established. In similarity variables, the mean Velocity profiles across the whole channel width outside viscous sublayers can be described by a one-parameter family of curves. The theoretical results obtained are in good agreement with available direct numerical simulation data.

Bernard O Bauer - One of the best experts on this subject based on the ideXlab platform.

  • analysis of Velocity profile measurements from wind tunnel experiments with saltation
    Geomorphology, 2004
    Co-Authors: Bernard O Bauer, Chris Houser, W G Nickling
    Abstract:

    Abstract Investigations of wind-field modification due to the presence of saltating sediments have relied heavily on wind tunnels, which are known to impose geometric constraints on full boundary layer development. There remains great uncertainty as to which portion of the vertical wind-speed profile to analyze when deriving estimates of shear Velocity or surface roughness length because the lower sections are modified to varying degree by saltation, whereas the upper segments may be altered by artificially induced wake-like effects. Thus, it is not obvious which of several alternative Velocity-profile parameterizations (e.g., Law of the Wall, Velocity Defect Law, Wake Law) should be employed under such circumstances. A series of experimental wind-tunnel runs was conducted across a range of wind speed using fine- and coarse-grained sand to collect high-quality, fine-resolution data within and above the saltation layer using thermal anemometry and ruggedized probes. After each run, the rippled bottom was fixed with fine mist, and the experiment repeated without saltation. The measured wind-speed profiles were analyzed using six different approaches to derive estimates of shear Velocity and roughness length. The results were compared to parameter estimates derived directly from sediment transport rate measurements, and on this basis, it is suggested that one of the six approaches is more robust than the others. Specifically, the best estimate of shear Velocity during saltation is provided by the logarithmic Law applied to the profile data within about 0.05 m of the bottom, despite the fact that this near-surface region is where profile modification by saltating sediments is most pronounced. Uncertainty remains as to whether this conclusion can be generalized to field situations because progressive downwind adjustments in the interrelationship between the saltation layer and the wind field are anticipated in wind tunnels, thereby confounding most analyses based on equilibrium assumptions.