The axisymmetric equivalent of Kolmogorov's equation

• Published in: The European physical journal. B, Condensed matter physics Vol. 23; no. 1; pp. 107 - 120
• Main Author: OULD-ROUISS, M
• Format: Journal Article
• Language: English
• Published: Les Ulis Springer 01.09.2001; Berlin EDP sciences; Springer-Verlag
• Subjects: Engineering Sciences; Exact sciences and technology; Fluid dynamics; Fluid mechanics; Fluids mechanics; Fundamental areas of phenomenology (including applications); Fundamentals; Isotropic turbulence; homogeneous turbulence; Mechanics; Physics; Turbulent flows, convection, and heat transfer; Tensors; Scaling laws; Theoretical study; Structure functions; Isotropic turbulence; Kolmogorov equation; Axial symmetry; Turbulence structure; Homogeneous turbulence
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1007/s100510170088

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.