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.

中文翻译：

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二维湍流中的混沌和信息

通过对不可压缩的均质和各向同性二维湍流进行大量完全解析的模拟，我们研究了最大Lyapunov指数，Kolmogorov-Sinai熵和吸引子尺寸的缩放行为。发现最大李雅普诺夫指数的标度与尺寸预测非常吻合。对于Kolmogorov-Sinai熵和吸引子维数的情况，发现简单的维数预测是不够的。发现了对系统大小和强制长度范围的依赖，表明存在非普遍行为。还讨论了这些结果对大气可预测性的适用性。