Self-similarity in fully developed homogeneous isotropic turbulence using the lyapunov analysis

Abstract

In this work, we calculate the self-similar longitudinal velocity correlation function and the statistics of the velocity difference, using the results of the Lyapunov analysis of the fully developed isotropic homogeneous turbulence just presented by the author in a previous work (de Divitiis, Theor Comput Fluid Dyn, doi:10.1007/s00162-010-0211-9). There, a closure of the von Kármán-Howarth equation is proposed and the statistics of velocity difference is determined through a specific statistical analysis of the Fourier-transformed Navier-Stokes equations. The longitudinal correlation functions correspond to steady-state solutions of the von Kármán- Howarth equation under the self-similarity hypothesis introduced by von Kármán. These solutions and the corresponding statistics of the velocity difference are numerically determined for different Taylorscale Reynolds numbers. The obtained results adequately describe the several properties of the fully developed isotropic turbulence. © The Author(s) 2011.