论文标题
地球物理流体动力学系统的协变量lyapunov载体和有限的时间正常模式
Covariant Lyapunov Vectors and Finite-Time Normal Modes for Geophysical Fluid Dynamical Systems
论文作者
论文摘要
分析了将地球物理流体动力学模型预测的不稳定性和适用于整体扰动的动力学载体。检查了协变量的lyapunov载体（CLV），正顺式Lyapunov载体（OLVS），单数矢量（SVS），浮点数向量和有限的时间正常模式（FTNMS）之间的关系，以进行周期性和隔离系统。在FTNM系数的相空间中，发现SV在特定时间与单位范围FTNM等同。在长期限制中，当SVS接近OLV时，Oseledec定理以及OLV和CLV之间的关系用于在此相位空间中将CLV与FTNM连接到FTNM。 CLV和FTNM的协变特性，以及它们的相位独立性，以及全球Lyapunov指数和FTNM增长率的规范独立性，都建立了它们的渐近收敛性。记录了这些结果有效性的动力学系统条件，尤其是Ergodicition，有限性和非单明性FTNM特征矩阵和传播器。检查了具有非排定OLV的系统，并检查了具有lyapunov频谱的系统，以及在存在诸如Rossby波之类的波浪中的规则，以及用于计算提出的前导CLV的系统，并有效的数值方法。介绍了Kolmogorov-Sinai熵产生和Kaplan-Yorke维度的规范独立时间版本。
Dynamical vectors characterizing instability and applicable as ensemble perturbations for prediction with geophysical fluid dynamical models are analysed. The relationships between covariant Lyapunov vectors (CLVs), orthonormal Lyapunov vectors (OLVs), singular vectors (SVs), Floquet vectors and finite-time normal modes (FTNMs) are examined for periodic and aperiodic systems. In the phase-space of FTNM coefficients, SVs are found to equate with unit norm FTNMs at certain times. In the long-time limit, when SVs approach OLVs, the Oseledec theorem and the relationships between OLVs and CLVs are used to connect CLVs to FTNMs in this phase-space. The covariant properties of both the CLVs, and the FTNMs, together with their phase-space independence, and the norm independence of global Lyapunov exponents and FTNM growth rates, establishes their asymptotic convergence. Conditions on the dynamical systems for the validity of these results, particularly ergodicity, boundedness and non-singular FTNM characteristic matrix and propagator, are documented. Systems with nondegenerate OLVs, and with degenerate Lyapunov spectrum as is the rule in the presence of waves such as Rossby waves, are examined, and efficient numerical methods for the calculation of leading CLVs proposed. Norm independent finite-time versions of the Kolmogorov-Sinai entropy production and Kaplan-Yorke dimension are presented.
