Self-Similar Solutions in the Homogeneous Isotropic Turbulence

TL;DR

This paper presents a theoretical analysis of self-similar solutions in isotropic homogeneous turbulence, calculating key correlation functions and energy spectra that align with observed turbulence properties.

Contribution

It introduces a new theoretical approach to derive self-similar solutions for turbulence, expanding understanding of steady-state behaviors in isotropic turbulence.

Findings

Numerically calculated correlation functions match experimental data.

Energy spectra exhibit expected self-similar scaling.

Steady-state solutions describe key turbulence properties.

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.