Abstract
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.
Highlights
The spectral and cospectral properties of the turbulence over a homogenized flat surface are well established
The three classical regions can be distinguished in the turbulent part of the atmospheric energy spectrum (Kaimal and Finnigan 1994): the energy-containing range, where energy is produced by buoyancy and shear, the inertial subrange, and the dissipation range
The stress cospectra normalized by auwGuw (Fig. 6) demonstrate many characteristics typical of those presented by Kaimal et al (1972); they converge to a single line in the inertial subrange and follow the −4/3 law; the separation according to ζ is evident in the statically stable state; the cospectral peak is reduced and shifted to higher frequencies as stability increases
Summary
The spectral and cospectral properties of the turbulence over a homogenized flat surface are well established. We analyze data from long-term (more than five years) measurements at two urban sites located in Łódz, central Poland, and compare spectral characteristics over the city with the universally accepted functions (Kaimal et al 1972). The motivation for such a validation is the differences in the structure of the atmospheric surface layer (ASL) between homogenous flat surfaces and the urban surface. The complex urban geometry makes the lower part of the surface layer, the roughness sub-layer (RSL), thicken over built-up areas, resulting in a relatively thin upper part of the ASL, the inertial sub-layer, where the Monin– Obukhov similarity theory applies. The procedure of data selection was the same as in Fortuniak et al (2013) and details about stationary tests and discussion on rejection of the data for selected wind directions can be found there
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