Statistical Properties of Decaying Two-Dimensional Turbulence

Abstract

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 q th 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 ∇×ω 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 ene...