Spectral scaling of unstably stratified atmospheric flows: Turbulence anisotropy and the low‐frequency spread

Abstract

Unstable surface‐layer velocity and temperature spectra, scaled using inertial subrange properties and Monin–Obukhov similarity theory, have been known to show a notable spread in low frequencies. Here, a large ensemble of 14 datasets, over relatively simple (from flat and homogeneous terrain to gentle slopes or valley floor) and very complex mountainous terrain (steep slopes, crater rim, mountain tops), is used to assess the reasons for this low‐frequency behaviour. Turbulence anisotropy is shown to be the primary factor accounting for the spread in the spectral density at the largest scales and the spectral peak position of streamwise and spanwise velocity spectra. On the other hand, the low‐frequency behaviour of surface‐normal spectra is dominated by stability effects, whereas for temperature spectra turbulence anisotropy and stability play a similar role. Using a combination of scaling relations for temperature and velocity variances as well as dissipation of turbulence kinetic energy and half the 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. These observations are valid over both simple and complex mountainous terrain, although variability of the largest scales of complex‐terrain datasets highlights the effect of processes other than turbulence anisotropy or stability. Finally, we provide some insights into the scalewise nature of anisotropic eddies under different stabilities.