论文标题
二维和三维湍流之间过渡的混乱度量
Chaotic measure of the transition between two and three dimensional turbulence
论文作者
论文摘要
使用直接数值模拟，我们研究了最大lyapunov指数在薄层湍流中的行为，其中系统的一个维度受到几何限制。已知这种系统通过混合的两维现象学状态从完全三维的湍流中展示出从完全三维的湍流过渡。在第二个过渡中，我们发现Lyapunov指数中的不连续跳跃表明这种系统的可预测性可能会发生巨大变化。在许多不同的湍流系统中可以看到这样的过渡，例如那些经历强旋转的系统，因此这些结果可能与复杂的现实世界流的可预测性有关。发现Lyapunov指数提供了对二维动力学过渡的特别清晰的量度。最后，研究了这些结果在高分辨率建模方面的应用。
Using direct numerical simulation we study the behavior of the maximal Lyapunov exponent in thin-layer turbulence, where one dimension of the system is constrained geometrically. Such systems are known to exhibit transitions from fully three dimensional turbulence through a mixed two and three dimensional phenomenology state and then onto fully two dimensional dynamics. We find a discontinuous jump in the Lyapunov exponent at this second transition implying the predictability of such systems can change dramatically. Such transitions are seen in a number of different turbulent systems, for example those undergoing strong rotation, hence these results may be relevant for the predictability of complicated real world flows. The Lyapunov exponent is found to provide a particularly clear measure of the transition to two dimensional dynamics. Finally, the application of these results to atmospheric predictability with regard to high-resolution modeling is examined.
