On the Possibility of Singular Low-Frequency Spectra and Lévy Law Persistence Statistics in the Planetary-Scale Turbulent Circulation

Abstract

Long-time integrations of general circulation models with constant forcing and idealized models of turbulent rotating discrete vortex flows in a planar dish have consistently yielded red ultralow-frequency spectra. A red spectrum having an integrable fractional-exponent singularity at the frequency origin is associated with occasional long-lasting random persistence intervals described by probability distributions with Levy law tails, suggesting this type of persistence distribution may be relevant to the planetary scale turbulence. Decade-length records of 200-mb wind velocity fluctuations from North American 12-h radiosonde data are examined for the presence of Levy statistics, and the convergence properties of errors in means and variances computed from finite length time-series samples containing random persistence intervals governed by Levy probability laws are compared with the convergence properties corresponding to the low-frequency white-noise hypothesis. Some implications for estimating climatic means and variances are discussed.