Self-Similar Solutions in the Homogeneous Isotropic Turbulence

Abstract

We calculate the self-similar longitudinal velocity correlation function, the energy spectrum and the corresponding other properties using a theory on the isotropic homogeneous turbulence just presented by the author in a previous work. The correlation functions correspond to steady-state solutions of the evolution equation under the self-similarity hypothesis introduced by von K\'arm\'an. These solutions are numerically calculated and the results adequately describe several properties of the isotropic turbulence.