Dynamical random multiplicative cascade model in 1+1 dimensions

TL;DR

This paper introduces a dynamical random multiplicative cascade model in 1+1 dimensions to describe the evolution of multifractal fields like turbulence, with analytical calculations of correlation functions.

Contribution

It presents a novel dynamical generalization of geometrical cascade models, capturing continuous stochastic evolution in space and time.

Findings

Derived two-point correlation functions for the model

Demonstrated the model's applicability to turbulence fields

Provided analytical tools for studying multifractal dynamics

Abstract

Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as for example the energy dissipation field of fully developed turbulence. A dynamical generalisation of these models is proposed, which describes the continuous and homogeneous stochastic evolution of the field in one space and one time dimension. Two-point correlation functions are calculated.