Cascade phenomenology (An Introduction to Complex Systems in Environment)

Mezemate Yacine, Schertzer Daniel

Multiplicative cascade processes are frequently used as phenomenological models for the study of a variety of complex systems exhibiting fractal/multifractal behavior. In particular the energy dissipation field of fully developed turbulent flows has been most successfully modeled in such terms, physically motivated by Richardson's poem of energy transfer from large to small scales by random breakups of eddies. Multiplicative cascade models are based on two assumptions: the existence of a scale-independent and statistical independence of the random weights at one breakup from those of any other breakup. During this lesson, we will give the principle of cascade and in which context were developed. We introduce three types of models that describe the cascade phenomenology. We finished with two exercises which allows us to play with -model and the -model. Module 4 of the course set "An Introduction to Complex Systems in Environment"