Nonlinear Generalization of Singular Vectors: Behavior in a Baroclinic Unstable Flow
Nonlinear Generalization of Singular Vectors: Behavior in a Baroclinic Unstable Flow
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DOI：
10.1175/2007jas2378.1
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发表时间：
2008-06
影响因子：
3.1
通讯作者：
O. Rivière;G. Lapeyre;O. Talagrand
中科院分区：
文献类型：
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作者：
O. Rivière;G. Lapeyre;O. Talagrand
摘要奇异向量(SV)分析已被证明有助于理解各种流动的线性不稳定性。当沿着特定解线性化模型的方程时，SVS是在给定时间间隔内具有最大放大速率的摄动。然而，推导SVS所需的线性近似具有很强的局限性，并且没有考虑非线性发展过程中存在的几种机制(如波-均流相互作用)。最近提出了一种新的技术，它允许用最优扰动的形式来推广完全非线性区域中具有最大放大率的SVS。在一个斜压不稳定的两层准地转模式的背景下，从结构和动力学的角度考察了非线性对这些非线性最优扰动[这里称为非线性奇异向量(NLSVs)]的影响。NLSVs与SVS的本质不同之处在于存在正的纬向平均切变和切变。
Abstract Singular vector (SV) analysis has proved to be helpful in understanding the linear instability properties of various types of flows. SVs are the perturbations with the largest amplification rate over a given time interval when linearizing the equations of a model along a particular solution. However, the linear approximation necessary to derive SVs has strong limitations and does not take into account several mechanisms present during the nonlinear development (such as wave–mean flow interactions). A new technique has been recently proposed that allows the generalization of SVs in terms of optimal perturbations with the largest amplification rate in the fully nonlinear regime. In the context of a two-layer quasigeostrophic model of baroclinic instability, the effect of nonlinearities on these nonlinear optimal perturbations [herein, nonlinear singular vectors (NLSVs)] is examined in terms of structure and dynamics. NLSVs essentially differ from SVs in the presence of a positive zonal-mean shear a...