On the use of Kolmogorov-Landau approach in deriving various correlation functions in 2-D incompressible turbulence

TL;DR

This paper employs the Kolmogorov-Landau approach to derive correlation functions in 2-D incompressible turbulence, simplifying existing methods and highlighting limitations in capturing certain scaling laws, with implications for turbulence theory.

Contribution

It demonstrates a simpler derivation of correlation functions in 2-D turbulence using Kolmogorov-Landau approach and discusses its limitations in obtaining the one-eighth law.

Findings

Derived correlation functions involving velocity and vorticity.

Showed the approach's inability to derive the one-eighth law.

Suggested possible logarithmic corrections in the enstrophy cascade.

Abstract

We look at various correlation functions, which include those that involve both the velocity and the vorticity fields, in 2-D isotropic homogeneous decaying turbulence.We adopt the more intuitive approach due to Kolmogorov (and subsequently, Landau in his text on fluid dynamics) and show that how the 2-D turbulence results, obtainable using other methods, may be established in a simpler way.Also, some experimentally verifiable correlation functions in the dissipation range have been derived for the same system.The paper also showcases the inability of the Kolmogorov-Landau approach to get the ``one-eighth law'' in the enstrophy cascade region.As discussed in the paper, this may raise the spectre of logarithmic corrections once again in 2-D turbulence.