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, σw/u*loc and σθ/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, σh/h (0.56 and 0.32). The results obey a semi-empirical relation of the form σw/u*loc = Φ(−ζloc)1/3 (ζloc = z′/Lloc, where z′ is the effective measurement height, Lloc is the local Obukhov length). The resultant extrapolated near-neutral constants depend on σh/h: (σw/u*loc)neutral = 1.04 and 1.27 for σh/h = 0.56 and 0.32, in the range − 0.01 > ζloc > − 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, ζloc > − 0.6 for σh/h = 0.32. The term σθ/u*loc follows the form Φ(−ζloc)− 1/3 with constants of (σθ/θ*loc)neutral = − 1.31 and − 1.34 for the two sectors, thus being independent of both σh/h and z/h. These findings show that similarity theory using local scales is applicable for determining σw and σθ in the convective roughness sublayer but depends on the vertical heterogeneity of the upwind sectors for σw, which only affects the near-neutral σw/u*loc constants. Copyright © 2012 Royal Meteorological Society