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

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