with the core vortex, provides the stirring for the initial increase of P. The mixing will reduce the P in the later stage. Figure 5 shows the time dependence of kinetic energy, enstrophy, and pa-linstrophy for the binary vortex experiment with Y = 5, r = 1/3, and A/R1 = 2.5 parameters. Two values of diffusivity v, 3.25 m2 s_1 and 6.5 m2 s_1, are employed in the experiments. The scale for the palinstrophy (kinetic energy and enstrophy) is on the left (right) side of the figure.

The near-conservation of the kinetic energy, the damping of the enstrophy field, and the initial increase (stirring) and the eventual decrease (mixing) of the palinstrophy field in the vortex interaction experiments, all possess the characteristics of two-dimensional turbulence. Batchelor (1969) argued that in the case of a nearly inviscid fluid (v small enough), the vor-ticity contours can pack close together before diffusion or mixing is effective. The closely packed contours increase \, and greatly enhance the palinstrophy. Even when v is small, the -2vP term on the right-hand side of (4) may not be small owing to the increase of palinstro-phy. We then have a significant enstrophy cascade. With a significant enstrophy cascade (area thus a smaller enstrophy later), the right hand side of the kinetic energy equation (3) is small and the kinetic energy is nearly conserved. This is the phenomenon of selective decay, i.e. the

0 0

Post a comment