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首页> 外文期刊>Journal of the Atmospheric Sciences >An Analytical Approach to the Determination of Optimal Perturbations in the Eady Model
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An Analytical Approach to the Determination of Optimal Perturbations in the Eady Model

机译：eady模型中最佳扰动测定的分析方法

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摘要

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.
机译：在曲金不稳定性的框架内，考虑了最大能量生长速率的最佳扰动的分析方法或最终和初始能量的比例。这种方法基于能量平衡方程和用于通过边缘rossby波（ERW）的叠加引起的能量函数产生的能量函数的明确表达式。相应的表达式是初始扰动参数的函数，并且最佳参数的确定减少了对极值上这些功能的研究。对于零电位涡度（PV）的扰动，大气层边界处的初始浮力分布的幅度和这些分布之间的相移用作参数。获得分析公式，用于最佳相移和能量比的最大值，从而确定它们对波数和优化时间的依赖性。还表明，最佳扰动总是具有相同的边界幅度。将最佳扰动的参数与日常正常模式的参数进行比较。建立只存在一个呈指数增长的正常模式，这是最佳的扰动。随着不稳定，ERW可以通过与初始涡流扰动（PV 0）的互动来兴奋。研究了通过PV初始奇异分布的ERWS激发的最佳状态。

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