Large Fluctuations in Stochastic Models of Turbulence

Abstract

This dissertation discusses the intermitency phenomenon in three models of turbulence, employing analytical and numerical techniques in the analysis of stochastic processes and the probability distributions which they induce. The initial chapters present a review of the statistical theory of turbulence and of statistical theory of fields as applied to out of equilibrium physics. Two chapters of the main text investigate the RFD model and the Burgers model through the Martin-Siggia-Rose-Janssen-de Dominicis (MSRJD) functional method. An analysis of the perturbative corrections corresponding to fluctuations around the instanton in both models is undertaken. The last chapter presents a stationary one-dimensional stochastic process as a model of Lagrangian pseudo-dissipation fluctuations. It is numerically verified that this process has a lognormal probability distribution and long range power-law correlations.