Comments on turbulence theory by Qian and by Edwards and McComb

TL;DR

This paper critically reexamines turbulence theories by Qian and Edwards & McComb, revealing that their assumptions for damping coefficients are unphysical, despite deriving similar spectral density equations compatible with Kolmogorov spectrum.

Contribution

It clarifies the assumptions behind two classical turbulence theories and demonstrates their unphysical nature, providing insight into their limitations.

Findings

Both theories yield identical spectral density equations.

The assumptions for damping coefficients are shown to be unphysical.

The theories are compatible with Kolmogorov spectrum despite their assumptions.

Abstract

We reexamine Liouville equation based turbulence theories proposed by Qian {[}Phys. Fluids \textbf{26}, 2098 (1983){]} and Edwards and McComb {[}J. Phys. A: Math. Gen. \textbf{2}, 157 (1969){]}, which are compatible with Kolmogorov spectrum. These theories obtained identical equation for spectral density $q(k)$ and different results for damping coefficient. Qian proposed variational approach and Edwards and McComb proposed maximal entropy principle to obtain equation for the damping coefficient. We show that assumptions used in these theories to obtain damping coefficient correspond to unphysical conditions.