Modelling velocity spectra in the lower part of the planetary boundary layer

Abstract

Principles used when constructing models for velocity spectra are reviewed. Based upon data from the Kansas and Minnesota experiments, simple spectral models are set up for all velocity components in stable air at low heights, and for the vertical spectrum in unstable air through a larger part of the planetary boundary layer. Knowledge of the variation with stability of the (reduced) frequency f, for the spectral maximum is utilized in this modelling. Stable spectra may be normalized so that they adhere to one curve only, irrespective of stability, and unstable w-spectra may also be normalized to fit one curve.The problem of using filtered velocity variances when modelling spectra is discussed. A simplified procedure to provide a first estimate of the filter effect is given.In stable, horizontal velocity spectra, there is often a 'gap' at low frequencies. Using dimensional considerations and the spectral model previously derived, an expression for the gap frequency is found.

Turbulence-Turbine Interaction: The Basis for the Development of the TurbSim Stochastic Simulator

“…Figures 9-8 and 9-9 show the resolved low-and high-range spectral peaks found for the NWTC ART and the virtual WindPACT turbine operating in the Lamar site environment using the same format. In agreement with Kaimal et al (1972) and Olesen et al (1984), the Lamar site vertical turbulence component exhibits the single spectral peak characteristic of flat, homogeneous terrain. Flow at the NWTC, however, like the wind farm, contains both low-and high-frequency peaks.…”

“…At the NWTC, we found that we could use the disk-averaged value based on the mean surface stress or u *o computed from Equation 9-1. The variation of u *D with u *o was found to be weakly correlated with Ri TL and is plotted in Figure 9 We used the Risø SL spectral models (Højstrup 1982;Olesen, Larsen, and Højstrup 1984) for unstable and stable flows as the basis spectrum description and derived empirical scaling ratios Ψ, Φ to adjust the amplitudes and positions of the spectral peaks to agree with the site-specific measurements. For flat, homogeneous terrain, Kaimal and Finnigan (1984) and Kaimal et al (1972) found that the u and v turbulent spectra in unstable flows could be modeled as the sum of two spectral peaks, as follows:…”

“…The target frequency low-and high-frequency range spectra were arrived at by scaling the Risø SL models (Højstrup 1982;Olesen, Larsen, and Højstrup 1984) with the amplitude and positional scaling factors Ψ and Φ, respectively, which are empirical functions of u * and z/L M-O derived for each of the wind speed and Ri TL ranges. The source of the u * and z/L scaling parameters varies with the site.…”

Modelagem Matemática em Turbulência Atmosférica

“…Uma expressão geral para o espectro da velocidade turbulenta adimensional na camada limite superficialé dada por [61] …”

“…onde a 1 = 0.5 ± 0.05 [75], α u = 1 e α v = α w = 4/3 [61] (ver também [75], página 134)); e, c u = 0.3 e c v = c w = 0.4. A função Φ é a dissipação adimensional.…”