THE LOCAL STRUCTURE OF ISOTROPIC TURBULENCE

Abstract

For the last three decades much attention has been focused on Kolmogoroff9s theory for the local structure of the isotropic turbulent field. Many investigators have tried experimental verification of the theory, but their results are considered insufficient. This is mainly due to the fact that, in experimental and industrial apparatus, turbulent Reynolds number Rex of fluid flow is generally not as high as Kolmogoroff assumed in his theory. In this study, relative velocity distribution in the isotropic turbulent field at low turbulent Reynolds number (Reλ = 30-100) is measured by hot-wire anemometry, and empirical equations of the velocity distribution are proposed. These equations contain two parameters which represent the characteristics of isotropic turbulence-Reλ and microscale λg of turbulence. Relations between λg and integral scale Ag, velocity-correlation function g(r) and one-dimensional power spectrum E1(k1) can be calculated from these equations. These calculated values agree well with experimental data obtained by many investigators. Furthermore, a few examples of the other calculated spectra of turbulence, such as three-dimensional power spectrum E(k) and energy-transfer functions F(k) and S(k), are also shown. The empirical equations are considered to be usefully applicable to turbulent flow over a wide range of Reλ, from 30 to 800 or more.