Remarks on Sedov-type Solution of Isotropic Turbulence

TL;DR

This paper revisits Sedov's classical solutions for isotropic turbulence, providing a more comprehensive analysis of self-preservation, energy decay, and turbulence features, with implications for understanding turbulence spectra and large-scale dynamics.

Contribution

It offers a deeper investigation into Sedov's solutions, extending the analysis of isotropic turbulence and connecting it with recent developments in turbulence theory.

Findings

New exact solutions for energy spectra in isotropic turbulence

Insights into scaling behavior and large-scale dynamics

Analysis of turbulence features across different wave number ranges

Abstract

The assumption of similarity and self-preservation, which permits an analytical determination of the energy decay in isotropic turbulence, has played an important role in the development of turbulence theory for more than half a century. Sedov (1944), who first found an ingenious way to obtain two equations from one. Nonethless, it appears that this problem has never been reinvestigated in depth subsequent to this earlier work. In the present paper, such an analysis is carried out, yielding a much more complete picture of self-preservation isotropic turbulence. Based on these exact solutions, some physically significant consequences of recent advances in the theory of self-preserved homogenous statistical solution of the Navier-Stokes equations are presented. New results could be obtained for the analysis on turbulence features, such as the scaling behavior, the spectrum, and also the large scale dynamics. The general energy spectra and their behavior in different wave number range are investigated.