Further Studies Of Atmospheric Turbulence In Layers Near The Surface: Scaling The Tke Budget Above The Roughness Sublayer

Frenzen, Paul D.; Vogel, Christoph

doi:10.1023/a:1018956931957

Cited by 29 publications

(46 citation statements)

References 25 publications

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“…The same general shape of the φ ε function has been reported previously (e.g. Högström 1990;Zhang and Park 1999;Frenzen and Vogel 2001;Su et al 2004;McNaughton 2006;Roth et al 2006). For urbanized areas, the dip observed between ζ = −0.5 and −0.1 is more pronounced in the data from Tokyo and Vancouver analyzed by Kanda et al (2002) than in our studies, whereas data from Basel (Roth et al 2006) show only a slight decrease for measurements above the roof level (z/z H = 1.32).…”

Section: The Spectra Of Velocity Componentssupporting

confidence: 91%

“…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: 78%

“…Garratt (1972) suggested for φ ε the same form as for the non-dimensional shear production φ m . Other methods of functional description of the experimental data of φ ε include a translated and rotated hyperbola (Frenzen and Vogel 2001) or a three sub-layer model for the convective case (Albertson et al 1997). …”

Section: Spectral and Cospectral Characteristicsmentioning

confidence: 99%

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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: 91%

Section: The Spectra Of Velocity Componentssupporting

confidence: 78%

Section: Spectral and Cospectral Characteristicsmentioning

confidence: 99%

See 1 more Smart Citation

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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“…These data have been gathered in the context of the CASES-99 project (Poulos et al, 2002). We will compare our findings with previously reported MOST functions for e and C T 2 ; for instance Wyngaard (1973), Ho¨gstro¨m (1990), Thiermann and Grassl (1992), Frenzen and Vogel (2001), and Pahlow et al (2001).…”

Section: Introductionmentioning

confidence: 62%

“…Several authors used Equation (5d) with different values for the constants c e1 and c e2 ; Wyngaard (1973) gave c e1 ¼ 1 and c e2 ¼ 5, Ho¨gstro¨m (1990) found c e1 ¼ 1.24 and c e2 ¼ 4.7, and, recently, Pahlow et al (2001) obtained c e1 ¼ 0.61 and c e2 ¼ 5. The original form of Equation (5c) given by Frenzen and Vogel (2001) reads f e ¼ (0.85 + 0.6f)(/ m ) f) with / m ¼ 1 + 5.3f. In Equation (5c), we inserted their / m function in the f e expression.…”

Section: Theorymentioning

confidence: 99%

Monin–Obukhov Similarity Functions of the Structure Parameter of Temperature and Turbulent Kinetic Energy Dissipation Rate in the Stable Boundary Layer

Hartogensis

Bruin

2005

Boundary-Layer Meteorol

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Abstract. The Monin-Obukhov similarity theory (MOST) functions f e and f T , of the dissipation rate of turbulent kinetic energy (TKE), e, and the structure parameter of temperature, C T 2 , were determined for the stable atmospheric surface layer using data gathered in the context of CASES-99. These data cover a relatively wide stability range, i.e. f ¼ z/L of up to 10, where z is the height and L the Obukhov length. The best fits were given by f e ¼ 0:8 þ 2:5f and f T ¼ 4:7½1 þ 1:6ðfÞ 2=3 ; which differ somewhat from previously published functions. e was obtained from spectra of the longitudinal wind velocity using a time series model (ARMA) method instead of the traditional Fourier transform. The neutral limit f e ¼ 0.8 implies that there is an imbalance between TKE production and dissipation in the simplified TKE budget equation. Similarly, we found a production-dissipation imbalance for the temperature fluctuation budget equation. Correcting for the production-dissipation imbalance, the 'standard' MOST functions for dimensionless wind speed and temperature gradients (/ m and / h ) were determined from f e and f T and compared with the / m and / h formulations of Businger and others. We found good agreement with the Beljaars and Holtslag [J. Appl. Meteorol. 30, 327-341 (1991)] relations. Lastly, the flux and gradient Richardson numbers are discussed also in terms of f e and f T .

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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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Further Studies Of Atmospheric Turbulence In Layers Near The Surface: Scaling The Tke Budget Above The Roughness Sublayer

Cited by 29 publications

References 25 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

Monin–Obukhov Similarity Functions of the Structure Parameter of Temperature and Turbulent Kinetic Energy Dissipation Rate in the Stable Boundary Layer

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

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