Spectral scaling of unstably-stratified atmospheric flows: understanding the low frequency spread of Kaimal model

For more than five decades, a notable spread in the low frequencies of velocity and temperature spectra, scaled using inertial subrange properties and Monin-Obukhov similarity theory, has been observed in unstable stratification. A large ensemble of 14 datasets, over relatively simple terrain (from flat and homogeneous to gentle slope or valley floor) and very complex terrain (steep slope, crater rim, mountain top), are used to assess the reasons of this low-frequency behaviour. Turbulence anisotropy is shown to be the primary factor influencing the spectral energy at the largest scales and the spectral peak position of streamwise and spanwise velocity spectra, with stability acting as a secondary factor. On the contrary, the low-frequency behaviour of surface-normal and temperature spectra is dominated by stability effects, while turbulence anisotropy plays a secondary role. These observations are valid over both simple and complex terrain, even though variability of the largest scales of complex terrain datasets integrate other processes not included in turbulence anisotropy or stability conditions. Using a combination of non-dimensional turbulence parameters - temperature and velocity variances as well as dissipation of turbulence kinetic energy and of temperature variance - and of a semi-empirical model provided in the literature, we are able to describe the behaviour of the velocity and temperature spectra with only turbulence anisotropy and stability as input parameters. Finally, the paper provides some insights into the nature of anisotropic eddies, as well as the relationship between the boundary layer height and the spectral behaviour.