On a symmetry of turbulence |
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Authors: | Scott Peckham Ed Waymire |
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Affiliation: | 1. CIRES, University of Colorado, 80309, Boulder, CO, USA 2. Department of Mathematics and Statistics, Oregon State University, 97331, Corvallis, OR, USA
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Abstract: | This paper presents results on symmetries of the spectrum of singularities for random cascades found in the statistical theory of turbulence. It is shown that empirical dimension curves possess a natural symmetry whose presence restricts the class of allowable probability distributions of the cascade generator in a simple manner. In particular, necessary and sufficient conditions on the probability distribution of the generator are obtained for symmetry of the singularity spectrum within a large class of cascade models. |
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