Homogeneous turbulence: an introductory review

Abstract

A brief review of developments in the theory of homogeneous turbulence over the last 50 years is given, many of these developments stemming from lectures and discussions at the 1961 Marseille Colloquium Mécanique de la Turbulence. The following topics are discussed: Kolmogorov’s 1961 lecture, intermittency and the finite-time singularity problem, the skewness factor paradox, Kraichnan’s direct interaction approximation, helicity and the dynamo problem, two-dimensional turbulence, rapid distortion theory and the passive and active scalar problems.

Keywords:

• Kolmogorov
• intermittency
• skewness
• helicity
• rapid distortion

Notes

1. Lecture delivered at the Turbulence Colloquium, Marseille 2011, commemorating Mécanique de la Turbulence, Marseille 1961.

2. A new ‘cross-independence’ closure theory has recently been proposed by Tatsumi [18], 54 years after the same author’s first paper on the decay of isotropic turbulence, a remarkable span of sustained investigation!

3. This paper and subsequent papers by the same authors were published in German, and were not very well known in the West until translated into English by Roberts and Stix [24], and subsequent publication of the book of Krause and Rädler [25].