Renormalization Group Analysis of Turbulent Hydrodynamics

TL;DR

This paper applies the exact renormalisation group to turbulent hydrodynamics, aiming to derive the scaling properties of structure functions and address deviations from Kolmogorov's predictions.

Contribution

It introduces a novel RG-based approach to analyze turbulence, providing initial numerical results and advancing theoretical understanding.

Findings

Initial numerical results obtained

Approach overcomes previous theoretical challenges

Potential to derive Kolmogorov deviations

Abstract

Turbulent hydrodynamics is characterised by universal scaling properties of its structure functions. The basic framework for investigations of these functions has been set by Kolmogorov in 1941. His predictions for the scaling exponents, however, deviate from the numbers found in experiments and numerical simulations. It is a challenge for theoretical physics to derive these deviations on the basis of the Navier-Stokes equations. The renormalisation group is believed to be a very promising tool for the analysis of turbulent systems, but a derivation of the scaling properties of the structure functions has so far not been achieved. In this work, we recall the problems involved, present an approach in the framework of the exact renormalisation group to overcome them, and present first numerical results.