Large Fluctuations in Stochastic Models of Turbulence

TL;DR

This dissertation explores the intermittency phenomenon in turbulence models using analytical and numerical methods, revealing large fluctuations and specific statistical properties in stochastic turbulence models.

Contribution

It introduces a detailed analysis of turbulence models with stochastic processes, employing the MSRJD functional method and numerical verification of distribution properties.

Findings

Lognormal distribution of pseudo-dissipation fluctuations

Long-range power-law correlations observed

Perturbative corrections analyzed around instantons

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.