An Analytical Approach to the Determination of Optimal Perturbations in the Eady Model
An Analytical Approach to the Determination of Optimal Perturbations in the Eady Model
复制标题
确定 Eady 模型中最优扰动的分析方法
DOI：
10.1175/jas-d-18-0089.1
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发表时间：
2018
影响因子：
3.1
通讯作者：
O. Chkhetiani
中科院分区：
文献类型：
--
作者：
M. Kalashnik;O. Chkhetiani
在斜压不稳定Eady模型的框架内，考虑了一种确定最佳扰动的分析方法，该方法具有最大的能量增长率或最终和初始能量的比率。这种方法是基于能量平衡方程和显式表达式的能量泛函所产生的扰动表示通过叠加的边缘Rossby波（ERWs）。相应的表达式是初始扰动参数的函数，最优参数的确定归结为研究这些函数的极值。对于位涡为零的扰动，大气层边界处的初始浮力分布的振幅和这些分布之间的相移作为参数。得到了最佳相移和最大能量比的解析公式，确定了它们对波数和优化时间的依赖关系。它还表明，最佳扰动总是有相等的边界振幅。最佳扰动的参数进行了比较与成长的正常模式的参数。建立了只存在一个指数增长的正常模式，这是最佳扰动。沿着不稳定性，ERW可通过其与初始涡扰动（PV ≥ 0）的相互作用而被激发。研究了PV初始奇异分布对ERW激发的最佳方案。
Within the framework of the baroclinic instability Eady model, an analytical approach to the determination of optimal perturbations with a maximum of the energy growth rate or the ratio of the final and initial energies is considered. This approach is based on the energy balance equation and explicit expressions for the energy functionals resulting from the perturbation representation by means of the superposition of the edge Rossby waves (ERWs). The corresponding expressions are functions of the parameters of the initial perturbation, and the determination of optimal parameters reduces to the study of these functions on an extremum. For perturbations with zero potential vorticity (PV), the amplitudes of the initial buoyancy distributions at the boundaries of the atmospheric layer and the phase shift between these distributions serve as parameters. Analytical formulas are obtained for the optimal phase shift and the maximum of the energy ratio, which determine their dependence on the wavenumber and optimization time. It is also shown that the optimal perturbations always have equal boundary amplitudes. The parameters of the optimal perturbations are compared with the parameters of the growing normal modes. It is established that there exists only one exponentially growing normal mode, which is the optimal perturbation. Along with the instability, the ERWs can be excited by their interaction with the initial vortex perturbations (PV ≠ 0). The optimal regime of ERWs excitation by the initial singular distribution of PV is investigated.
斜压初值问题的解释：具有非零内部 PV 梯度的简单基本状态的结果
影响因子：
3.1
作者：
Frame T
通讯作者：
Frame T