Instanton calculus in shell models of turbulence
It has been shown recently that the intermittency of the Gledzer-Ohkitani-Yamada (GOY) shell model of turbulence has to be related to singular structures whose dynamics in the inertial range includes interactions with a background of fluctuations. In this paper we propose a statistical theory of these objects by modeling the incoherent background as a Gaussian white-noise forcing of small strength Gamma. A general scheme is developed for constructing instantons in spatially discrete dynamical systems and the Cramer function governing the probability distribution of effective singularities of exponent z is computed up to first order in a semiclassical expansion in powers of Gamma. The resulting predictions are compared with the statistics of coherent structures deduced from full simulations of the GOY model at very high Reynolds numbers.
Daumont
I
Centre de Recherches sur les Tres Basses Temperatures-CNRS, Laboratoire Conventionne Avec l'Universite Joseph Fourier, Boiinsertion markte Postale 166, 38042 Grenoble Cedex 9, France and Ecole Normale Superieure de Lyon, Laboratoire.
Dombre
T
Gilson
JL