Second-order spectral local isotropy of the humidity and temperature fields in an urban area



A theoretical and experimental analysis of the humidity and temperature spatial differentials (δ/δxj,) in an urban area is presented. The local isotropy form of the spectra of the streamwise and vertical differentials of a scalar field is derived. The experimental results for the humidity and temperature fields in the lowest part of the urban boundary layer are in satisfactory agreement (at least in form under stable conditions) with the local isotropy model indicating that these fields can be locally isotropic. A strong anisotropy was observed at small wavenumbers of the vertical differentials spectra and it is probably connected with surface-layer plumes. The analysis of the humidity and temperature differentials is extended to their co-spectra and the spectra of the vertical differentials are compared to the streamwise ones. The comparison of the structure parameters of the temperature or the humidity field in the streamwise and the vertical direction, estimated using a spectral and a variance (structure function) method, showed no systematic departure from the isotropic prediction of equality.