Overall self-similar decay of two-dimensional turbulence

The statistics of two-dimensional decaying turbulence are investigated by t he use of direct numerical simulation in a periodic box. A number of cases are systematically compared in which the incompressible Navier-Stokes equat ion is solved on various resolutions and fur various Reynolds numbers start ing with random velocity fields of a prescribed energy spectrum. It is obse rved that the statistics are contaminated rapidly by the periodicity of the flow field which blocks the transfer of velocity fluctuations towards larg er scales. At large Reynolds numbers the enstrophy spectrum decays similarl y in time throughout the whole wavenumber range and the enstrophy decreases inversely proportionally to time.