# An Introduction to Large Deviations and Equilibrium Statistical Mechanics for Turbulent Flows

## TL;DR

This paper introduces how large deviation theory and equilibrium statistical mechanics can be used to understand and predict the emergence of organized coherent structures in two-dimensional turbulent and geophysical flows.

## Contribution

It applies principles of equilibrium statistical mechanics and large deviation theory to analyze and predict large-scale energy condensation and coherent structures in turbulent flows.

## Key findings

- Energy condenses at large scales in 2D turbulence
- Coherent structures can be predicted using statistical mechanics
- Large deviation theory provides a framework for flow analysis

## Abstract

Two-dimensional turbulent flows, and to some extent, geophysical flows, are systems with a large number of degrees of freedom, which, albeit fluctuating, exhibit some degree of organization: coherent structures emerge spontaneously at large scales. In this short course, we show how the principles of equilibrium statistical mechanics apply to this problem and predict the condensation of energy at large scales and allow for computing the resulting coherent structures. We focus on the structure of the theory using the language of large deviation theory.