Abstract
We present results from an ensemble of 50 runs of two-dimensional hydrodynamic turbulence with spatial resolution of grid points and from an ensemble of 10 runs with 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 law, with negative flux, together with a 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 . 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.
- Received 18 May 2011
DOI:https://doi.org/10.1103/PhysRevE.87.033002
©2013 American Physical Society