An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation
An in-depth numerical study of the two-dimensional Kuramoto–Sivashinsky equation
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二维 Kuramoto-Sivashinsky 方程的深入数值研究
DOI：
10.1098/rspa.2014.0932
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
D. T. Papageorgiou
中科院分区：
文献类型：
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作者：
A. Kalogirou;E. Keaveny;D. T. Papageorgiou
一维Kuramoto-Sivashinsky方程（1D KSE）是最著名和研究最多的偏微分方程之一。随着畴长的增加，它表现出通过各种分叉出现的时空混沌。有几个值得注意的分析研究，旨在了解如何将此属性扩展到两个空间维度的情况。在这项研究中，我们进行了广泛的数值研究的Kuramoto-Sivashinsky方程（2D KSE），以补充这项分析工作。我们详细探讨了混沌解决方案的统计和分类的解决方案，出现的域大小的平凡的解决方案是不稳定的，长时间的动态是完全二维的。虽然我们发现1D KSE的许多特征，包括能量如何随系统大小缩放，可以延续到2D的情况下，但我们也注意到一些差异，包括不通过周期加倍的各种混沌路径。
The Kuramoto–Sivashinsky equation in one spatial dimension (1D KSE) is one of the most well-known and well-studied partial differential equations. It exhibits spatio-temporal chaos that emerges through various bifurcations as the domain length increases. There have been several notable analytical studies aimed at understanding how this property extends to the case of two spatial dimensions. In this study, we perform an extensive numerical study of the Kuramoto–Sivashinsky equation (2D KSE) to complement this analytical work. We explore in detail the statistics of chaotic solutions and classify the solutions that arise for domain sizes where the trivial solution is unstable and the long-time dynamics are completely two-dimensional. While we find that many of the features of the 1D KSE, including how the energy scales with system size, carry over to the 2D case, we also note several differences including the various paths to chaos that are not through period doubling.