Table of Contents
Physics Research International
Volume 2013 (2013), Article ID 872796, 20 pages
http://dx.doi.org/10.1155/2013/872796
Research Article

Renormalisation Group Analysis of Turbulent Hydrodynamics

Institut für Theoretische Physik, Universität Münster, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany

Received 29 December 2012; Accepted 29 April 2013

Academic Editor: Uwe Claus Tauber

Copyright © 2013 Dirk Barbi and Gernot Münster. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 renormalization 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.