Eur. Phys. J. B 15, 339-347 (2000)
https://doi.org/10.1007/s100510051135

Axisymmetric form of Kármán-Howarth equation and its limiting forms

Laboratoire de Génie des Procédés, bâtiment Lavoisier, Université de Marne-la-Vallée, 77420 Champs-sur-Marne, France

Received: 1 July 1999
Revised: 9 November 1999
Published online: 15 May 2000

Abstract

Kinematics and dynamics of homogeneous axisymmetric turbulence have been derived with the assumption that the properties of the turbulence are invariant with respect to rotation about a preferred direction λ. In particular, the "axisymmetric" equivalent of Karman-Howarth "isotropic" equation is derived using Lindborg's representation of the two-point correlation tensors of homogeneous axisymmetric turbulence. When the more constraining assumption of isotropy is made, this equation reduces to the well-known Karman-Howarth equation. There are two interesting limiting forms of the axisymmetric Karman-Howarth equation: the axisymmetric form of the energy balance equation and the axisymmetric form of the vorticity balance equation.