论文标题
准线性动力学系统及其统计封闭的不等式
Non-equivalence of quasilinear dynamical systems and their statistical closures
论文作者
论文摘要
人们普遍认为，动态系统的统计封闭理论提供了与前者得出的管理动力学方程相当的统计。在这里，我们在应用于2D流体动力学系统的广泛使用的均值准线性（QL）近似的背景下演示了反例。我们将QL数值模拟的统计数据与通过二阶封闭（CE2）封闭的累积扩展获得的QL数值模拟的统计数据。我们观察到，尽管CE2是QL动力学的确切统计闭合，但其预测与相同参数值的QL解决方案的统计数据不同意。这些分歧归因于QL方程中不可用的CE2中第二个累积动力学的不稳定性，我们将其称为不稳定性。
It is widely believed that statistical closure theories for dynamical systems provide statistics equivalent to those of the governing dynamical equations from which the former are derived. Here, we demonstrate counterexamples in the context of the widely used mean-field quasilinear (QL) approximation applied to 2D fluid dynamical systems. We compare statistics of QL numerical simulations with those obtained by direct statistical simulation via a cumulant expansion closed at second order (CE2). We observe that, though CE2 is an exact statistical closure for QL dynamics, its predictions disagree with the statistics of the QL solution for identical parameter values. These disagreements are attributed to instabilities, which we term rank instabilities, of the second cumulant dynamics within CE2 that are unavailable in the QL equations.
