Direct determination of the f(alpha) singularity spectrum and its application to fully developed turbulence

Details Direct determination of the f(alpha) singularity spectrum and its application to fully developed turbulence Direct determination of the f(alpha) singularity spectrum and its application to fully developed turbulence

Nov 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989phrva..40.5284c&link_type=abstract

Physical Review A - General Physics, 3rd Series (ISSN 0556-2791), vol. 40, Nov. 1, 1989, p. 5284-5294. Research supported by NSF

Mathematics

83

Chaos, Fractals, Singularity (Mathematics), Spectral Methods, Turbulent Flow, Atmospheric Circulation, Finite Difference Theory, Legendre Functions, Turbulence Models

Scientific paper

This paper focuses on a method proposed for determining f(alpha) - the singularity spectrum of a multifractal - directly from experimental data, without first calculating the 'generalized dimensions' and applying the usual Legendre transforms. The method, which is based on theorems by Shannon, Eggelston, and Billingsley is described, and it is applied to one-dimensional cuts of the dissipation field of fully developed turbulence in laboratory and atmospheric flows. The accuracy of this method can be understood in terms of computation of conventional thermodynamic quantities in microcanonical and canonical ensembles. Comparisons with other direct and indirect methods of computing f(alpha) are made.

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