Turbulence under a magnifying glass

TL;DR

This paper provides an introductory overview of open problems in fully developed turbulence, covering theoretical, statistical, and field-theoretic approaches, highlighting current challenges and research directions.

Contribution

It offers a comprehensive synthesis of turbulence theories, including recent developments like the inverse renormalization group, for researchers entering the field.

Findings

Discussion of existence of solutions to hydrodynamical equations

Analysis of Kolmogorov scaling and its breakdown in passive scalar models

Comparison of turbulence with field theory approaches

Abstract

This is an introductory course on the open problems in the theory of fully developed turbulence. It discusses: 1. hydrodynamical equations, 2. existence of solutions, 3. statistical description of turbulent flows, 4. Kolmogorov scaling theory, 5. functional approach to turbulence: similarities and differences with field theory, 6. breakdown of the Kolmogorov theory in a passive scalar model, 7. inverse renormalization group.