A critical note on one-eighth law in 2D turbulence

TL;DR

This paper critically examines the proofs of the one-eighth law in 2D turbulence, providing a rigorous proof for unforced high Reynolds number cases and deriving an exact expression for velocity correlations in the enstrophy cascade regime.

Contribution

It offers a critical review and a rigorous proof of the one-eighth law in unforced 2D turbulence, along with an exact correlation expression for enstrophy cascade.

Findings

Proof of the one-eighth law for unforced 2D turbulence.

Derived exact expression for the time derivative of velocity correlation.

Reconciled previous attempts to prove the law.

Abstract

We critically revisit the various attempts to prove one eighth law in 2D turbulence and reconcile them. Herein, the one-eight law has been proved for unforced 2D incompressible high Reynolds number turbulence. An exact expression of the time derivative of two-point second order velocity correlation function is also derived for the enstrophy cascade dominated regime.