On streamwise velocity spectra models with fractal and long-memory effects

Using theoretical arguments, we present two novel spectrum models of the streamwise velocity component with robust correlation structures, which account for and decouple the fractal dimension and Hurst effect. The formulations that use isotropic concepts are adapted from the modern probability theory using the so-called generalized Cauchy and Dagum models, which belong to wide-sense-stationary random fields. A complementary inspection of these two models with field data from a met-tower-mounted sonic anemometer located within the atmospheric surface layer reveals good agreement and better performance than other conventionally used isotropic-based models of streamwise velocity spectra. The fractal dimension, D, of both models is consistent with the well-known Kolmogorov -5/3 power law in the inertial sub-range. For completeness, the study includes a derivation of the explicit forms of the energy spectral densities of the Cauchy and Dagum covariances.