It is shown that the Weierstrass-Mandelbrot function simulates the irregularity in a turbulent velocity record and yields correct forms for the energy and dissipation spectra. In particular, the universal properties of a corresponding multi-fractal function are demonstrated by showing its ability to reproduce and explain turbulent flow spectra measured near the walls of straight and curved channels and in the obstructed space between a pair of disks corotating in an axisymmetric enclosure. The simulation capabilities of the multi-fractal function strongly suggest thai turbulence is fractal in the frequency range of the turbulent energy spectrum where the slope of the logarithm of the spectrum, G, is -3 < G < -1. The scale-independent frequency range of the energy spectrum correctly represented by the multi-fractal function includes the isotropic dissipation subrange (-3 < G < -5/3), the inertial subrange (G = -5/3), and the "inner" portion of the anisotropic large-scale subrange ( -5/3 < G < -1).
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.