Turbulence variances in the convective urban roughness sublayer: an application of similarity theory using local scales

Abstract

Similarity theory using local scales was applied to the normalized standard deviation of the vertical wind component, w, and potential temperature, θ, σ_w/u_*loc and σ_θ/θ_*loc, where u_*loc and θ_*loc are the friction velocity and temperature and ‘loc’ refers to variables that are locally measured. These data were obtained in a tropical city under convective atmospheric conditions within the roughness sublayer. The following parameters were assessed based on the upwind characteristics of the site, denoted as ‘sectors’: the non-dimensional height, z/h (1.16 and 1.20), and the non-dimensional vertical heterogeneity, σ_h/h (0.56 and 0.32). The results obey a semi-empirical relation of the form σ_w/u_*loc = Φ(−ζ_loc)^1/3 (ζ_loc = z′/L_loc, where z′ is the effective measurement height, L_loc is the local Obukhov length). The resultant extrapolated near-neutral constants depend on σ_h/h: (σ_w/u_*loc)_neutral = 1.04 and 1.27 for σ_h/h = 0.56 and 0.32, in the range − 0.01 > ζ_loc > − 20. Spectral analysis of w reveals a separation of the spectral power at low non-dimensional frequencies (f < 0.03) with increasing deviation as the atmosphere approaches neutral conditions, ζ_loc > − 0.6 for σ_h/h = 0.32. The term σ_θ/u_*loc follows the form Φ(−ζ_loc)− ^1/3 with constants of (σ_θ/θ_*loc)_neutral = − 1.31 and − 1.34 for the two sectors, thus being independent of both σ_h/h and z/h. These findings show that similarity theory using local scales is applicable for determining σ_w and σ_θ in the convective roughness sublayer but depends on the vertical heterogeneity of the upwind sectors for σ_w, which only affects the near-neutral σ_w/u_*loc constants. Copyright © 2012 Royal Meteorological Society