Global and Local Scaling of the Enstrophy Dissipation Rate in Two-Dimensional Turbulence

Abstract

We investigate the global and local structure of the enstrophy dissipation rate in two-dimensional turbulence simulated on 512² mesh points from a multifractal point of view. The generalized dimensions D_q could be determined for any positive value of q. D_q for q≤ q₀ (-- 4) reflect a global nature of the dissipative structure and may be universal. On the other hand, D_q for q>> q₀ put the emphasis on the local structure and they may not be universal. We confirm that the scaling holds on smaller squares chosen arbitrarily. Dividing the system into 64 squares of size of 64 mesh points, we obtain the distribution of D_q; it has a broad spectrum. Finally, the most intense region is found to consist of many layers of positive and negative vorticity.