Inverse cascade behavior in freely decaying two-dimensional fluid turbulence

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 the same initial integral scale, energy, enstrophy, and Reynolds number. When both ensemble and time averaged, an 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 on the connections between decaying and forced turbulence and recent controversies in experimental studies of two-dimensional and magnetohydrodynamic turbulent flows.