In the context of the analysis of the chaotic properties of homogeneous and isotropic turbulence, direct numerical simulations are used to study the fluctuations of the finite-time Lyapunov exponent (FTLE) and its relation to the Reynolds number, the lattice size, and the choice of the steptime used to compute the Lyapunov exponents. The results show that using the FTLE method produces Lyapunov exponents that are remarkably stable under the variation of the steptime and lattice size. Furthermore, it reaches such stability faster than other characteristic quantities such as energy and dissipation rate. These results remain even if the steptime is made arbitrarily small. A discrepancy is also resolved between previous measurements of the dependence on the Reynolds number of the Lyapunov exponent. The signal produced by different variables in the steady state is analyzed, and the self-decorrelation time is used to determine the run time needed in the simulations to obtain proper statistics for each variable. Finally, a brief analysis on magnetohydrodynamic flows is also presented as an extension to recent work, which shows that the Lyapunov exponent is still a robust measure in the simulations, although the Lyapunov exponent scaling with the Reynolds number is significantly different from that of magnetically neutral hydrodynamic fluids.

中文翻译：

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李雅普诺夫指数在均匀和各向同性湍流中的涨落

在分析均质和各向同性湍流的混沌特性的背景下，直接数值模拟用于研究有限时间李雅普诺夫指数（FTLE）的涨落及其与雷诺数，晶格大小和选择的关系计算李雅普诺夫指数的步长。结果表明，使用FTLE方法产生的Lyapunov指数在步长和晶格尺寸的变化下非常稳定。此外，它比其他特征量（例如能量和耗散率）更快达到这种稳定性。即使步长被任意地减小，这些结果仍然保留。先前对Lyapunov指数的雷诺数的依赖性的测量结果之间的差异也得到解决。分析稳态下不同变量产生的信号，并使用自解相关时间来确定仿真所需的运行时间，以获得每个变量的适当统计信息。最后，还对磁流体动力流动进行了简要分析，作为对近期工作的扩展，这表明，尽管雷诺数的李雅普诺夫指数标度与磁中性的标度存在显着差异，但李雅普诺夫指数仍是模拟中的一种可靠的度量。流体动力流体。