Statistical Properties of Decaying Two-Dimensional Turbulence

We investigate the temporal development of the statistical properties of two-dimensional incompressible turbulence simulated for a long time. First, we obtain information on the evolving microscopic vortical structure by inspecting the time variation of qth order fractal dimensions of the enstrophy dissipation rate. The conclusion drawn from such an inspection is consistent with a picture given by Kida (J. Phys. Soc. Jpn. 54 (1985) 2840); in the first stage the del x omega field grows up in the most advantageous spots of the initial configuration, leading to the very intermittent state, and the energy spectrum is near k-4. Then the turbulence enters the less intermittent stage with the spectrum k-3. Second, we measure the probability density functions (PDF) of the vorticity, its increment over a distance and the enstrophy dissipation rate. The PDFs of the vorticity increment over a small separation and the enstrophy dissipation rate are found to be quite similar to those of the velocity increment and the energy dissipation rate in three dimensions.