Inverse cascade behavior in freely decaying two-dimensional fluid turbulence

TL;DR

This study demonstrates inverse energy cascade behavior in freely decaying two-dimensional turbulence, showing that energy transfer to larger scales occurs even without external forcing, with specific spectral laws observed.

Contribution

It provides the first comprehensive numerical evidence of inverse cascade in decaying 2D turbulence with high-resolution simulations, linking decaying and forced turbulence behaviors.

Findings

Inverse cascade observed in decaying turbulence

Energy spectrum follows k^(-5/3) law at large scales

Enstrophy flux is positive at small scales

Abstract

We present results from an ensemble of 50 runs of two-dimensional hydrodynamic turbulence with spatial resolution of 2048^2 grid points, and from an ensemble of 10 runs with 4096^2 grid points. All runs in each ensemble have random initial conditions with same initial integral scale, energy, enstrophy, and Reynolds number. When both ensemble- and time-averaged, inverse energy cascade behavior is observed, even in the absence of external mechanical forcing: the energy spectrum at scales larger than the characteristic scale of the flow follows a k^(-5/3) law, with negative flux, together with a k^(-3) law at smaller scales, and a positive flux of enstrophy. The source of energy for this behavior comes from the modal energy around the energy containing scale at t=0. The results shed some light into connections between decaying and forced turbulence, and into recent controversies in experimental studies of two-dimensional and magnetohydrodynamic turbulent flows.