Instanton calculus in shell models of turbulence

It has been shown recently that the intermittency of the Gledzer-Ohkitani-Y amada (GOY) shell model of turbulence has to be related to singular structu res whose dynamics in the inertial range includes interactions with a backg round of fluctuations. In this paper we propose a statistical theory of the se objects by modeling the incoherent background as a Gaussian white-noise forcing of small strength Gamma. A general scheme is developed for construc ting instantons in spatially discrete dynamical systems and the Cramer func tion governing the probability distribution of effective singularities of e xponent z is computed up to first order in a semiclassical expansion in pow ers 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.