Local Imbalance of Turbulent Kinetic Energy in the Surface Layer

Li, Xiangyi; Zimmerman, Neil M.; Princevac, Marko

doi:10.1007/s10546-008-9304-z

Cited by 22 publications

(43 citation statements)

References 49 publications

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“…The constants a i estimated in this way for Łódź are close to those given by Kaimal et al (1972) Oncley et al 1996;Frenzen and Vogel 2001;Andreas et al 2006;Li et al 2008;Leonardi and Castro 2010;Kanda et al 2013) suggest that κ could be lower than 0.4, especially over rough surfaces (κ decreases with increasing roughness Reynolds number). The Kolmogorov constant, α u , also ranges from 0.36 to 0.56 (Högström 1990), which introduces additional imprecision in the estimation of φ ε (0).…”

Section: The Spectra Of Velocity Componentssupporting

confidence: 77%

“…Our approximation of b 1 = 3.45 is lower than the value deduced from φ ε = φ m − ζ for a typical range of slopes of φ m in stable stratification (e.g. Table 1 in Li et al 2008). The majority of other studies report higher values for this parameter.…”

Section: The Spectra Of Velocity Componentscontrasting

confidence: 60%

“…However, there is some empirical evidence that production is not locally dissipated (Högström 1990;Vogel 1992, 2001;Albertson et al 1997;Pahlow et al 2001;Li et al 2008) and Eq. 3 should be modified to…”

Section: Spectral and Cospectral Characteristicsmentioning

confidence: 99%

“…where ψ = φ ε (ζ = 0) is referred to as the imbalance coefficient varying in the range from 0.61 to 1.24 (Li et al 2008). Still, the functional form of the non-dimensional dissipation rate of TKE can be derived on the basis of the dimensionless wind shear function, φ m .…”

Section: Spectral and Cospectral Characteristicsmentioning

confidence: 99%

“…Hicks 1978;De Bruin et al 1993). Klipp and Mahrt (2004) and Baas et al (2006) showed that φ m is influenced by this effect; both the high scatter and the increase, less rapid than linear, of φ m with stability in very (u, v, w) for two sites in Łódź; uvwLNband-averaged function calculated separately for each wind component and for each site; SD-band-averaged function from all data; fit 1-the function φ ε = (1 − 37ζ ) −1/4 − ζ (for ζ < 0), φ ε = 1 + 3.45ζ (for ζ > 0); fit 2-the function φ 2/3 ε = 1 + 1.56ζ 3/5 (for ζ > 0); Low panel b EQL2008-different form of φ ε calculated as φ ε = φ m − ζ with various φ m taken after Table 1 by Li et al (2008); grey area-range of results Su et al 2004 stable conditions can be a spurious result of self-correlation between variables due to the occurrence of the friction velocity on both axes. In our case, the friction velocity also affects both variables.…”

Section: The Spectra Of Velocity Componentsmentioning

confidence: 99%

See 4 more Smart Citations

Selected Spectral Characteristics of Turbulence over an Urbanized Area in the Centre of Łódź, Poland

Fortuniak

Pawlak

2014

Boundary-Layer Meteorol

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We present the turbulence spectra and cospectra derived from more than five years of eddy-covariance measurements at two urban sites in Łódź, central Poland. The fast response wind velocity components were obtained using sonic anemometers placed on narrow masts at 37 and 42 m above ground level. The analysis follows Kaimal et al. (Q J R Meteorol Soc 98:563-589, 1972) who established the spectral and cospectral properties of turbulent flow in atmospheric surface layer on the basis of the Kansas experiment. Our results illustrate many features similar to those of Kaimal et al., but some differences are also observed. The velocity (co)spectra from Łódź show a clear inertial subrange with −2/3 slope for spectra and −4/3 slope for cospectra. We found that an appropriate stability function for the non-dimensional dissipation of turbulent kinetic energy calculated from spectra in the inertial subrange differs from that of Kaimal et al., and it can be satisfactorily estimated with the assumption of local equilibrium using standard functions for the non-dimensional shear production. A similar function for the cospectrum corresponds well to Kaimal et al. for unstable and weakly stable conditions. The (co)spectra normalized by their spectral values in the inertial subrange are in general similar to those of Kaimal et al., but they peak at lower frequencies in strongly stable conditions. Moreover, our results do not confirm the existence of a clear "excluded region" at low frequencies for the transition from stable to unstable conditions, for longitudinal and lateral wind components. The empirical models of Kaimal et al. with adjusted parameters fit well to the vertical velocity spectrum and the vertical momentum flux cospectrum. The same type of function should be used for longitudinal and lateral wind spectra because of their sharper peak than occurs for the Kansas data. Finally, it should be stressed that the above relationships are well-defined for averaged values. The results for individual 1-h periods are very scattered and can be significantly different from the generalized functions.

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Section: The Spectra Of Velocity Componentssupporting

confidence: 77%

Section: The Spectra Of Velocity Componentscontrasting

confidence: 60%

Section: Spectral and Cospectral Characteristicsmentioning

confidence: 99%

Section: Spectral and Cospectral Characteristicsmentioning

confidence: 99%

Section: The Spectra Of Velocity Componentsmentioning

confidence: 99%

See 3 more Smart Citations

Selected Spectral Characteristics of Turbulence over an Urbanized Area in the Centre of Łódź, Poland

Fortuniak

Pawlak

2014

Boundary-Layer Meteorol

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Turbulence kinetic energy budget in the stable boundary layer over a heterogeneous surface

Babić

Rotach

2018

Quart J Royal Meteoro Soc

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This study presents turbulence kinetic energy (TKE) budget terms above tall, deciduous walnut canopy in the wintertime stable boundary layer (SBL) and makes a comparison to well‐known results of horizontally homogeneous and flat (HHF) terrain. Turbulence measurements performed at five levels above the canopy height (approximately h=18 m) enable the investigation of joint effect of the roughness sublayer (RSL) and the transition layer on the TKE budget terms. Each term of the TKE budget is investigated within the framework of local similarity theory. Kolomogorov's similarity hypothesis assumes local isotropy within the inertial subrange. Thoroughly testing the local isotropy hypothesis for the present dataset results in a ratio of the horizontal spectral densities (Sv/Su) approaching 4/3, while the ratio of the vertical to the longitudinal spectral density (Sw/Su) is less than the canonical value of 4/3 (even less than 1) for all levels indicating anisotropic turbulence even at very small scales above the canopy. As a consequence, estimated values of TKE dissipation rate (ε) from the vertical component are smaller than those obtained from the horizontal velocity components. This finding has a direct influence on the applicability of classical Kansas spectral models valid for HHF terrain as well as on the budget of wind variances. Additionally, the behavior of the non‐dimensional gradient of mean wind speed is tested with regard to conformity to z‐less scaling requirements (i.e. linear dependence on stability). It is confirmed that a stability threshold (such as Rf > 0.25, where Rf is the flux Richardson number) is a stronger determinant of z‐less behavior than the existence of a well‐defined inertial subrange ‐ opposite to observations in the SBL over ideal flat surfaces. Finally, the local equilibrium between the production and destruction of TKE within the RSL and transition layer is analyzed.

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Computational Fluid Dynamics model of stratified atmospheric boundary‐layer flow

et al. 2013

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For wind resource assessment, the wind industry is increasingly relying on computational fluid dynamics models of the neutrally stratified surface‐layer. So far, physical processes that are important to the whole atmospheric boundary‐layer, such as the Coriolis effect, buoyancy forces and heat transport, are mostly ignored. In order to decrease the uncertainty of wind resource assessment, the present work focuses on atmospheric flows that include stability and Coriolis effects. The influence of these effects on the whole atmospheric boundary‐layer are examined using a Reynolds‐averaged Navier–Stokes k‐ ε model. To validate the model implementations, results are compared against measurements from several large‐scale field campaigns, wind tunnel experiments, and previous simulations and are shown to significantly improve the predictions. Copyright © 2013 John Wiley & Sons, Ltd.

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Local Imbalance of Turbulent Kinetic Energy in the Surface Layer

Cited by 22 publications

References 49 publications

Selected Spectral Characteristics of Turbulence over an Urbanized Area in the Centre of Łódź, Poland

Selected Spectral Characteristics of Turbulence over an Urbanized Area in the Centre of Łódź, Poland

Turbulence kinetic energy budget in the stable boundary layer over a heterogeneous surface

Computational Fluid Dynamics model of stratified atmospheric boundary‐layer flow

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