Developing Homogeneous Isotropic Turbulence

TL;DR

This paper studies the transient evolution of energy spectra in 3D homogeneous isotropic turbulence using the EDQNM model, revealing self-similar behavior with a steeper spectrum than Kolmogorov's.

Contribution

It demonstrates the self-similar transient evolution with a non-trivial scaling exponent prior to the Kolmogorov spectrum using a closure model.

Findings

Transient spectrum exhibits self-similarity of the second kind.

Scaling exponent of the transient spectrum is non-trivial.

DNS data limitations prevent conclusive detection of the phenomenon.

Abstract

We investigate the self-similar evolution of the transient energy spectrum which precedes the establishment of the Kolmogorov spectrum in homogeneous isotropic turbulence in three dimensions using the EDQNM closure model. The transient evolution exhibits self-similarity of the second kind and has a non-trivial dynamical scaling exponent which results in the transient spectrum having a scaling which is steeper than the Kolmogorov $k^{-5/3}$ spectrum. Attempts to detect a similar phenomenon in DNS data are inconclusive owing to the limited range of scales available.