Recent spectra of atmospheric turbulence

Abstract

SUMMARYSpectra of atmospheric turbulence recently measured at various heights and sites under a variety of stability conditions have been analysed and compared. The results are :(i) In regions over which the spectra obey -5/3 power laws, the ratio of the lateral to the longitudinal spectra shows fair agreement with the 4/3 ratio predicted by the Kolmogorov hypothesis for the inertial sub-range. The vertical-longitudinal ratio has a similar tendency.Dissipation rates computed from the longitudinal spectra seem to be consistent with the hypothesis that dissipation is balanced by the total production of mechanical and convective turbulent energy, provided that the turbulence is in equilibrium. In transition from rough to smooth terrain, dissipation exceeds the other terms.(iii) Vertical-velocity spectra obey Monin-Obukhov similarity theory up to a height of about 50 m. Their shapes are reasonably uniform, the major change with stability being a change of scale of the wave number axis, i.e., any characteristic nondimensional wave number is a function of z / L only. This function appears to be the same as the relation between the normalized dissipation and z/L. These results are consistent with previously measured Kolmogorov constants and with measured ratios of standard deviation of vertical velocity to friction velocity. Up to about a height of 50 m the wavelengths of the maxima of the logarithmic spectra increase linearly with height and more slowly thereafter, up to about 300 m. The spectra in stable air above 50 m suggest the existence of a buoyant sub-range.(iv) Longitudinal spectra do not obey similarity theory in a number of ways. The wavelengths do not scale with height, and there may be differences between sites when the spectra are plotted in similarity coordinates.(v) Spectra over the sea seem to have relatively more energy at low frequencies than those over land.(ii)

Some Features of the Spatial Structures of the Surface Layer Turbulence in the High Wind Condition

“…The peak reduced frequency * max decreases with height according to a power law (e.g. Soma (1964), Berman (1965), Busch andPanofsky (1968), Fichtl (1968), Shiotani (1969), Naito and Kondo (1974)). Shiotani (1969) shows that the following relation agrees with the data including Satoura wind data in the range of mean wind of 10-20 m/ sec;…”

On the length‐scale of the wind profile

“…During the last 50 years, efforts have been made to study the spectral characteristics of atmospheric turbulence (Busch and Panofsky, 1968;Kaimal et al, 1972;Højstrup, 1982;Mann, 1994) and the behaviour of the lengthscale of turbulence with height and atmospheric stability (Kaimal et al, 1972;Caughey and Palmer, 1979;Højstrup et al, 1997;Lenderink and Holslag, 2004;Peña et al, 2010b). The investigation of the length-scale of the wind profile was initiated by Prandtl (1925), who introduced the concept of the mixing length when analyzing mean velocity profiles in laboratory flows.…”

First Observations of Energy Budget and Bulk Fluxes at Ny Ålesund (Svalbard) during a 2010 Transition Period as Analyzed with the BEAR Station

“…can be applied (see Businger et al [20]). The behaviour of these Monin-Obukhov functions is largely described in the literature, see, for example, Busch [21]. They can be expressed as follows:…”