On the displacement height in the logarithmic velocity profile

Jackson, Peter S.

doi:10.1017/s0022112081002279

Cited by 497 publications

(355 citation statements)

References 13 publications

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“…1 depicts the canonical structure of the atmospheric surface layer, with the roughness elements located on the substrate surface z = 0. 1 The so-called displacement height is denoted by d (Jackson 1981;Raupach and Legg 1984). MOST (including the logarithmic law of the wall) is valid within the inertial sublayer (ISL), where the lower limit of the ISL is z * (= αh) and the upper limit is usually taken as the 10% of the boundary-layer height.…”

Section: Figmentioning

confidence: 99%

A Cautionary Note on the Use of Monin–Obukhov Similarity Theory in Very High-Resolution Large-Eddy Simulations

Basu

Lacser

2017

Boundary-Layer Meteorol

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In several recent large-eddy simulation studies, the lowest grid level was located well within the roughness sublayer. Monin-Obukhov similarity-based boundary conditions cannot be used under this scenario, and in this note we elaborate on this fundamental problem and suggest potential solutions.Keywords Inertial sublayer · Large-eddy simulation · Monin-Obukhov similarity theory · Roughness sublayer · Surface layerIn the era of petascale computing, very high-resolution (the grid size, Δ = O(1) m or finer) large-eddy simulation (LES) of atmospheric boundary-layer (ABL) flows is gradually becoming a norm. For example, in a recent study (Sullivan et al. 2016), Δ = 0.39m was utilized in the idealized simulation of the stable boundary layer. It is a well-known fact that all the contemporary LES codes utilize the conventional Monin-Obukhov similarity theory (MOST) as lower boundary conditions (e.g., Heus et al. 2010;Maronga et al. 2015). It is also common knowledge (e.g., Lumley and Panofsky 1964;Monin and Yaglom 1971;Wyngaard 2010) that MOST is only valid for heights z z • , where z • is the aerodynamic roughness length. MOST is not applicable for z < αh, where h denotes the height of the roughness elements. Typically, α is assumed to be between 2 and 5 based on laboratory studies (see Raupach et al. 1991, and references therein). Unfortunately, a number of recent LES studies (e.g., Beare et al. 2006;Basu et al. 2011; Maronga 2014;Sullivan et al. 2016;Udina et al.

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Section: Figmentioning

confidence: 99%

A Cautionary Note on the Use of Monin–Obukhov Similarity Theory in Very High-Resolution Large-Eddy Simulations

Basu

Lacser

2017

Boundary-Layer Meteorol

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“…The downward shift of the log-region is represented by the roughness length y 0 in meteorology, or equivalently by ∆U + in the engineering community. d is referred to as the zero-plane displacement, which Jackson (1981) proposed to be interpreted as the height at which the mean surface drag appears to act.…”

Section: Introductionmentioning

confidence: 99%

Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

Placidi

Ganapathisubramani

2015

J. Fluid Mech.

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Citation: Placidi, M. & Ganapathisubramani, B. (2015). Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers. Journal of Fluid Mechanics, 782, pp. 541-566. doi: 10.1017Mechanics, 782, pp. 541-566. doi: 10. /jfm.2015 This is the accepted version of the paper.This version of the publication may differ from the final published version. Experiments were conducted in the fully-rough regime on surfaces with large relative roughness height (h/δ ≈ 0.1, where h is the roughness height and δ is the boundary layer thickness). The surfaces were generated by distributed LEGO TM bricks of uniform height, arranged in different configurations. Measurements were made with both floating-element drag-balance and high-resolution particle image velocimetry on six configurations with different frontal solidity, λ F , at fixed plan solidity, λ P , and vice versa, for a total of twelve rough-wall cases. Results indicate that the drag reaches a peak value λ F ≈ 0.21 or a constant λ P = 0.27, whilst it monotonically decreases for increasing values of λ P for a fixed λ F = 0.15. This is in contrast with previous studies in the literature based on cube roughness that show a peak in drag for both λ F and λ P variations. The influence of surface morphology on the depth of the roughness sublayer (RSL) is also investigated. Its depth is found to be inversely proportional to the roughness length, y 0 . A decrease in y 0 is usually accompanied by a thickening of the the RSL and vice-versa. Proper orthogonal decomposition analysis was also employed. The shapes of the most energetic modes calculated using the data across the entire boundary layer are found to be selfsimilar across the twelve rough-walls cases, however, when the analysis is restricted to the roughness sublayer, differences that depend on the wall morphology are apparent. Moreover, the energy content of the POD modes within the RSL suggest that the effect of increased frontal solidity is to redistribute the energy towards the larger-scales (i.e. larger portion of energy is within the first few modes) whilst the opposite is found for variation of plan solidity. Permanent

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“…Physically, the zero-plane displacement (displacement height), d 0 , is defined for a virtual wall boundary layer to reproduce flow statistics above the canopy roughness sublayer. The definition based on the mean shear stress links the displacement height to the vertical distribution of the mean canopy drag within the canopy (Thom 1971;Jackson 1981). Consequently the variability in the drag-wind relationship is expected to cause variability in the displacement height that directly affects the flux-gradient relationship above the canopy.…”

Section: Introductionmentioning

confidence: 99%

Estimating the Instantaneous Drag–Wind Relationship for a Horizontally Homogeneous Canopy

Pan

Chamecki

Nepf

2016

Boundary-Layer Meteorol

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The mean drag-wind relationship is usually investigated assuming that field data are representative of spatially-averaged metrics of statistically stationary flow within and above a horizontally homogeneous canopy. Even if these conditions are satisfied, large-eddy simulation (LES) data suggest two major issues in the analysis of observational data. Firstly, the streamwise mean pressure gradient is usually neglected in the analysis of data from terrestrial canopies, which compromises the estimates of mean canopy drag and provides misleading information for the dependence of local mean drag coefficients on local velocity scales. Secondly, no standard approach has been proposed to investigate the instantaneous drag-wind relationship, a critical component of canopy representation in LES. Here, a practical approach is proposed to fit the streamwise mean pressure gradient using observed profiles of the mean vertical momentum flux within the canopy. Inclusion of the fitted mean pressure gradient enables reliable estimates of the mean drag-wind relationship. LES data show that a local mean drag coefficient that characterizes the relationship between mean canopy drag and the velocity scale associated with total kinetic energy can be used to identify the dependence of the local instantaneous drag coefficient on instantaneous velocity. Iterative approaches are proposed to fit specific models of velocity-dependent instantaneous drag coefficients that represent the effects of viscous drag and the reconfiguration of flexible canopy elements. LES data are used to verify the assumptions and algorithms employed by these new approaches. The relationship between mean canopy drag and mean velocity, which is needed in models based on the Reynolds-averaged Navier-Stokes equations, is parametrized to account for both the dependence on velocity and the contribution from velocity variances. Finally, velocity-dependent drag coefficients lead to significant variations of the calculated displacement height and roughness length with wind speed. B Marcelo Chamecki

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On the displacement height in the logarithmic velocity profile

Cited by 497 publications

References 13 publications

A Cautionary Note on the Use of Monin–Obukhov Similarity Theory in Very High-Resolution Large-Eddy Simulations

A Cautionary Note on the Use of Monin–Obukhov Similarity Theory in Very High-Resolution Large-Eddy Simulations

Effects of frontal and plan solidities on aerodynamic parameters and the roughness sublayer in turbulent boundary layers

Estimating the Instantaneous Drag–Wind Relationship for a Horizontally Homogeneous Canopy

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