https://doi.org/10.1140/epjb/e2006-00213-y
Multidimensional infinitely divisible cascades
Application to the modelling of intermittency in turbulence
LIMOS UMR CNRS 6158-Université Blaise Pascal, 63173 Aubière Cedex, France
Corresponding author: a pchainai@isima.fr
Received:
16
December
2005
Revised:
3
April
2006
Published online:
2
June
2006
The framework of infinitely divisible scaling was first developed to analyse the statistical intermittency of turbulence in fluid dynamics. It also reveals a powerful tool to describe and model various situations including Internet traffic, financial time series, textures ... A series of recent works introduced the infinitely divisible cascades in 1 dimension, a family of multifractal processes that can be easily synthesized numerically. This work extends the definition of infinitely divisible cascades from 1 dimension to d dimensions in the scalar case. Thus, a class of models is proposed both for data analysis and for numerical simulation in dimension d≥1. In this article, we give the definitions and main properties of infinitely divisible cascades in d dimensions. Then we focus on the modelling of statistical intermittency in turbulent flows. Several other applications are considered.
PACS: 02.50.Ey – Stochastic processes / 05.45.Df – Fractals / 47.53.+n – Fractals in fluid dynamics / 47.27.E- – Turbulence simulation and modelling
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2006