Simplification and Validation of a Spectral-Tensor Model for Turbulence Including Atmospheric Stability

Abstract

A spectral-tensor model of non-neutral, atmospheric-boundary-layer turbulence is evaluated using Eulerian statistics from single-point measurements of the wind speed and temperature at heights up to 100 m, assuming constant vertical gradients of mean wind speed and temperature. The model has been previously described in terms of the dissipation rate ϵ, the length scale of energy-containing eddies L, a turbulence anisotropy parameter Γ, the Richardson number Ri, and the normalized rate of destruction of temperature variance ηθ≡ ϵθ/ ϵ. Here, the latter two parameters are collapsed into a single atmospheric stability parameter z / L using Monin–Obukhov similarity theory, where z is the height above the Earth’s surface, and L is the Obukhov length corresponding to { Ri, ηθ}. Model outputs of the one-dimensional velocity spectra, as well as cospectra of the streamwise and/or vertical velocity components, and/or temperature, and cross-spectra for the spatial separation of all three velocity components and temperature, are compared with measurements. As a function of the four model parameters, spectra and cospectra are reproduced quite well, but horizontal temperature fluxes are slightly underestimated in stable conditions. In moderately unstable stratification, our model reproduces spectra only up to a scale ∼ 1 km. The model also overestimates coherences for vertical separations, but is less severe in unstable than in stable cases.