[La structure statistique spatio-temporelle du champ de dissipation turbulente et sa représentation stochastique sous forme de chaos multiplicatif gaussien]
The present article concerns the stochastic modeling of the turbulent dissipation field and in particular its temporal evolution. To do so, we will be calling for a random distribution, ubiquitous in several aspects of physics and probability theory, known as the Gaussian Multiplicative Chaos (GMC), that takes its roots in the phenomenology of fluid turbulence. Firstly introduced by Mandelbrot, shortly after Yaglom’s discrete multiplicative cascade models, and rigorously studied by Kahane, the GMC appears as an appropriate statistically homogeneous model of the turbulent dissipation field. In this article, we will be recalling several ingredients of the associated turbulent phenomenology and its stochastic representation as a GMC, and propose a generalization to a spatio-temporal framework. All along the presentation of known properties in space, and in order to support new propositions concerning the temporal evolution, we will be calling for a comparison against direct numerical simulations of the Navier–Stokes equations extracted from a publicly accessible database.
Cet article porte sur la modélisation stochastique du champ de la dissipation turbulente et, en particulier, de son évolution temporelle. Pour ce faire, nous ferons appel à une distribution aléatoire, omniprésente dans plusieurs domaines de la physique et de la théorie des probabilités, connue sous le nom de « chaos multiplicatif gaussien » (GMC), qui trouve ses racines dans la phénoménologie de la turbulence des fluides. Introduit pour la première fois par Mandelbrot, peu après les modèles de cascades multiplicatives discrètes de Yaglom, et étudié de manière rigoureuse par Kahane, le GMC apparaît comme un modèle approprié de la nature statistiquement homogène du champ de dissipation. Dans cet article, nous rappellerons plusieurs éléments de la phénoménologie associée de la turbulence des fluides et de sa représentation stochastique sous forme de GMC, et proposerons une généralisation à un cadre spatio-temporel. Tout au long de la présentation des propriétés connues dans l’espace, et afin d’étayer de nouvelles propositions concernant l’évolution temporelle, nous ferons appel à une comparaison avec des simulations numériques directes des équations de Navier–Stokes extraites d’une base de données librement accessible.
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Mots-clés : Turbulence, modélisation stochastique, équations de Navier–Stokes
Wandrille Ruffenach 1 ; Laurent Chevillard 1 , 2
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Wandrille Ruffenach; Laurent Chevillard. The spatio-temporal statistical structure of the turbulent dissipation field and its stochastic representation as a Gaussian multiplicative chaos. Comptes Rendus. Physique, Volume 27 (2026), pp. 275-305. doi: 10.5802/crphys.283
@article{CRPHYS_2026__27_G1_275_0,
author = {Wandrille Ruffenach and Laurent Chevillard},
title = {The spatio-temporal statistical structure of the turbulent dissipation field and its stochastic representation as a {Gaussian} multiplicative chaos},
journal = {Comptes Rendus. Physique},
pages = {275--305},
year = {2026},
publisher = {Acad\'emie des sciences, Paris},
volume = {27},
doi = {10.5802/crphys.283},
language = {en},
}
TY - JOUR AU - Wandrille Ruffenach AU - Laurent Chevillard TI - The spatio-temporal statistical structure of the turbulent dissipation field and its stochastic representation as a Gaussian multiplicative chaos JO - Comptes Rendus. Physique PY - 2026 SP - 275 EP - 305 VL - 27 PB - Académie des sciences, Paris DO - 10.5802/crphys.283 LA - en ID - CRPHYS_2026__27_G1_275_0 ER -
%0 Journal Article %A Wandrille Ruffenach %A Laurent Chevillard %T The spatio-temporal statistical structure of the turbulent dissipation field and its stochastic representation as a Gaussian multiplicative chaos %J Comptes Rendus. Physique %D 2026 %P 275-305 %V 27 %I Académie des sciences, Paris %R 10.5802/crphys.283 %G en %F CRPHYS_2026__27_G1_275_0
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