Filtered deterministic waves and analysis of the fractal dimension of the components of the wind velocity

Abstract

The difficulty in developing models for waves in turbulent flows is a key problem in the analysis of the complexity of turbulence. We present a method to find and filter perturbations that are generated by the flow of deterministic waves from the power spectrum in the atmospheric boundary layer (ABL). The perturbation model proposed assumes that the amplitude and frequency of such waves decay with time exponentially. For illustrative purposes, we apply the technique to three time series of wind velocities obtained with a sonic anemometer. This analytical procedure allows us to filter waves of the proposed structure with a 99% significance level in the power spectrum. We have applied the same method to 540 such wind series, all painting similar results. We then compare the fractal dimension of the original series to those from which the waves have been removed. We find that the fractal dimension of the filtered waves is slightly less than that of the original series. Finally, we consider the fractal dimension of the studied series as a function of the length-scales and dissipation rate of kinetic energy per unit mass. Our results suggest an increase of fractal dimension with both length-scale and dissipation rate of kinetic energy.