Bishop, MAOughton, SeanParashar, TNPerrott, YC2026-08-112026-08-112026-02-02Bishop, M. A., Oughton, S., Parashar, T. N., & Perrott, Y. C. (2026). Direct power spectral density estimation from structure functions without Fourier transforms. Physics of Fluids, 38(2). https://doi.org/10.1063/5.03105611070-6631https://hdl.handle.net/10289/18525Second-order structure functions and power spectral densities are popular tools in the study of statistical properties across scales, particularly for the analysis of turbulent flows. Although intimately related, analyses primarily use one or the other. We introduce a framework for estimating the power spectrum using the second-order structure function without applying Fourier transforms—enabling one to take advantage of the real-space structure function calculations. We validate and showcase this method, comparing it to classical Fourier power spectrum estimates determined from analytical calculations, fractional Brownian motion, turbulence simulations, and space-physics and astrophysical observations of turbulence. We show that this method is able to robustly obtain the expected power law behavior where we use turbulence ranges as test-cases.enAttribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/mathematicsJournal Article10.1063/5.03105611089-76664012 Fluid Mechanics and Thermal Engineering40 Engineering51 Physical Sciences4012 Fluid Mechanics and Thermal Engineering40 Engineering51 Physical Sciences40 Engineering49 Mathematical sciences51 Physical sciences