https://doi.org/10.1140/epjb/e2008-00218-6
Apparent scale correlations in a random multifractal process
1
Corporate Technology, Information&Communications, Siemens AG, 81730 München, Germany
2
Thiele Centre for Applied Mathematics in Natural Science, Aarhus University, 8000 Aarhus, Denmark
Corresponding author: a jochen.cleve@siemens.com
Received:
13
February
2008
Revised:
10
April
2008
Published online:
6
June
2008
We discuss various properties of a homogeneous random multifractal process, which are related to the issue of scale correlations. By design, the process has no built-in scale correlations. However, when it comes to observables like breakdown coefficients, which are based on a coarse-graining of the multifractal field, scale correlations do appear. In the log-normal limit of the model process, the conditional distributions and moments of breakdown coefficients reproduce the observations made in fully developed small-scale turbulence. These findings help to understand several puzzling empirical details, which have been extracted from turbulent data already some time ago.
PACS: 47.27.eb – Statistical theories and models / 47.27.Gs – Isotropic turbulence; homogeneous turbulence / 47.53.+n – Fractals in fluid dynamics / 02.50.Ey – Stochastic processes / 02.50.Ga – Markov processes
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2008
