Cascade phenomenology

Introduction

The first description of the turbulence cascade came with the intuitive scheme of Richardson. This was later formalized by the self-similarity hypothesis ([Kolmogorov, A. N, 1941][1]). The first attempt to provide a quantitative description of the Richardson cascade was made by [Yaglom, A. M, 1966][2] and [Gurvich, A. S., & Yaglom, A. M, 1967][3].

Principle of the Yaglom's cascadeInformationInformation[4]

Different discrete and continuous cascade models have been introduced to describe intermittent fluxes. A first family of models is composed of discrete models, for which the scale ratio between a structure and the daughter structure is a discrete integer. Due to their discrete nature, these models are not realistic but have been introduced for their simplicity and ability to reproduce experimental

intermittency. These models include the :

  • β-model

  • α-model

  • p-model

  • ...., etc.

  1. [Kolmogorov, A. N, 1941]

    Kolmogorov, A. N. (1941, January). The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. In Dokl. Akad. Nauk SSSR (Vol. 30, No. 4, pp. 301-305).

  2. [Yaglom, A. M, 1966]

    Yaglom, A. M. (1966, July). The influence of fluctuations in energy dissipation on the shape of turbulence characteristics in the inertial interval. In Soviet Physics Doklady (Vol. 11, p. 26).

  3. [Gurvich, A. S., & Yaglom, A. M, 1967]

    Gurvich, A. S., & Yaglom, A. M. (1967). Breakdown of eddies and probability distributions for smallā€scale turbulence. Physics of Fluids (1958-1988), 10(9), S59-S65.

  4. Schmitt, F. G. Une équation stochastique pour l'intermittence de la turbulence: un processus multifractal causal et lognormal.

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