Enstrophy dissipation and vortex thinning for the incompressible 2D Navier-Stokes equations

TL;DR

This paper investigates how vortex thinning influences enstrophy dissipation in 2D Navier-Stokes turbulence, revealing that vortex thinning leads to enhanced dissipation with a slower decay rate than previously expected.

Contribution

It demonstrates that vortex thinning causes increased enstrophy dissipation with a decay rate slower than Re^{-1}, advancing understanding of dissipation mechanisms in 2D turbulence.

Findings

Vortex thinning induces enhanced enstrophy dissipation.

Dissipation decay rate is slower than Re^{-1}.

Supports the inverse energy cascade mechanism.

Abstract

By direct numerical simulation to the two-dimensional Navier-Stokes equations with small-scale forcing and large-scale damping, Xiao-Wan-Chen-Eyink (2009) found an evidence that inverse energy cascade may proceed with the vortex thinning mechanism. On the other hand, Alexakis-Doering (2006) calculated upper bound of the bulk averaged enstrophy dissipation rate of the steady-state two dimensional turbulence. {In this paper, we show that vortex thinning induces enhanced dissipation with strictly slower vanishing order of the enstrophy dissipation than $Re^{-1}$.}