A Promising Quantitative Measure for Comparison of Power Spectral Densities

The development of temporally resolved simulations and experiments has made the comparison of power spectral densities a growing concern. Assessing the spectra and their similarity is vital for many applications, especially for the validation of temporally resolved simulations. Nowadays, the analysis of spectra in fluid dynamics is usually limited only to assessing whether their slopes fit the theoretical expectations regarding the slope of the inertial region of the turbulence cascade. This approach is used even in cases where no expected slope can be derived. The assessment of similarity is then left to the subjective feeling of ”similar” With the increasing use of high-fidelity results in engineering practice, this approach falls behind. In this contribution, we propose a new method based on the distribution of energy in the spectra to replace the human factor. This method is tested on several spectra that exhibit common properties faced in nowadays problems, such as multiple peaks or inertial region of the turbulence cascade. Presented test results suggest that when combined with classical approaches of fluid mechanics and signal processing, this new method can form the basis for quantitative comparisons of power spectral densities.