Chaos and information in two-dimensional turbulence

By performing a large number of fully resolved simulations of incompressible homogeneous and isotropic two-dimensional turbulence, we study the scaling behavior of the maximal Lyapunov exponent, the Kolmogorov-Sinai entropy, and attractor dimension. The scaling of the maximal Lyapunov exponent is found to be in good agreement with the dimensional predictions. For the cases of the Kolmogorov-Sinai entropy and attractor dimension, the simple dimensional predictions are found to be insufficient. A dependence on the system size and the forcing length scale is found, suggesting nonuniversal behavior. The applicability of these results to atmospheric predictability is also discussed.