Turbulence de Burgers en 1D : un cas modèle pour la théorie de Kolmogorov

Alexandre Boritchev

doi:10.5802/slsedp.31

Turbulence de Burgers en 1D : un cas modèle pour la théorie de Kolmogorov

Alexandre Boritchev ¹

¹ CMLS Ecole Polytechnique 91128 Palaiseau Cedex France

Séminaire Laurent Schwartz — EDP et applications (2011-2012), Talk no. 40, 13 p.

Abstract

Nous nous intéressons ici à la turbulence de Burgers 1D, ou « Burgulence ». Nous présentons des résultats valables pour l’équation de Burgers généralisée périodique stochastique 1D :

u_{t} + f^{'} (u) u_{x} = ν u_{x x} + η, t \geq 0, x \in S^{1} = ℝ / ℤ,

où $η (t, x)$ est une force de type bruit blanc en $t$ et lisse en $x$ . Plus précisément, nous estimons les normes de Sobolev et les quantités à petite échelle analogues à celles qui sont intéressantes pour l’étude de la turbulence hydrodynamique, telles que les incréments et le spectre d’énergie. Les résultats exposés ici se trouvent dans l’article [7].

DOI: 10.5802/slsedp.31

Author's affiliations:

Alexandre Boritchev ¹

¹ CMLS Ecole Polytechnique 91128 Palaiseau Cedex France

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Alexandre Boritchev. Turbulence de Burgers en 1D : un cas modèle pour la théorie de Kolmogorov. Séminaire Laurent Schwartz — EDP et applications (2011-2012), Talk no. 40, 13 p. doi : 10.5802/slsedp.31. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.31/

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