Spectra and correlation functions of surface layer atmospheric turbulence in unstable thermal stratification

Abstract

A surface layer of the Earth’s atmosphere above flat homogeneous ground on hot summer days is the most easily accesible example of an unstably stratified boundary layer. The mean air temperature T = T(z) is here decreasing with height z and the mean density ρ = ρ(z) is increasing with z. As it is customary in the micrometeorology the atmospheric surface layer (ASL) will be defined as the lower air layer of the thickness z _s ≤ 0.1z _i (where z _i is the height of the lower edge of the inversion layer where T(z)is increasing with z) satisfying the condition that the turbulence fluxes of momentum and temperature τ = ρ<—uw>and Q = <wt> can be considered as independent of z. (In this paper the turbulent fluctuations of longitudinal, i.e. directed along the mean wind, lateral, and vertical velocity components, and temperature are denoted by u = u ₁, v = u ₂, w = u ₃, and t = u ₄, and the angular brackets symbolize averaging). It is known that in the middle latitudes on a hot summer day z _s ≈ 50m and z _i ≈ 1km. The thin lowest sublayer, where the molecular transfers and ground roughness affect directly the turbulence structure, will be always excluded from the consideration. Then the statistical characteristics of the surface-layer turbulence can be assumed to depend only on the following three dimensional parameters: τ / ρ (or equivalently, u _* = (τ / ρ)^1/2), Q, and the buoyancy parameter β = g γ, where g is the acceleration due to gravity and γ is the coefficient of thermal expansion (wich is equal to 1/T ₀ for an ideal gas, T ₀ being the mean absolute temperature of the surface layer).