Eur. Phys. J. B 23, 107-120 (2001)
https://doi.org/10.1007/s100510170088

The axisymmetric equivalent of Kolmogorov's equation

Université de Marne-la-Vallée, 77454 Marne-la-Vallée Cedex 2, France

Corresponding author: ^a ould@univ-mlv.fr

Received: 20 October 2000
Revised: 25 May 2001
Published online: 15 September 2001

Abstract

A type of turbulence which is next to local isotropy in order of simplicity, but which corresponds more closely to turbulent flows encountered in practice, is locally axisymmetric turbulence. A representation of the second and third order structure function tensors of homogeneous axisymmetric turbulence is given. The dynamic equation relating the second and third order scalar structure functions is derived. When axisymmetry turns into isotropy, this equation is reduced to the well-known isotropic result: Kolmogorov's equation. The corresponding limiting form is also reduced to the well-known isotropic limiting form of Kolmogorov's equation. The new axisymmetric and theoretical results may have important consequences on several current ideas on the fine structure of turbulence, such as ideas developed by analysis based on the isotropic dissipation rate ^∈iso or such as extended self similarity (ESS) and the scaling laws for the n-order structure functions.