Eur. Phys. J. B 51, 229-243 (2006)
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

Abstract

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.