Exact instantaneous optimals in the non-geostrophic Eady problem and the detrimental effects of discretization
Exact instantaneous optimals in the non-geostrophic Eady problem and the detrimental effects of discretization
复制标题
非地转 Eady 问题中的精确瞬时最优以及离散化的有害影响
DOI：
10.1007/s00162-019-00488-w
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发表时间：
2018
影响因子：
3.4
通讯作者：
I. Grooms
中科院分区：
文献类型：
--
作者：
W. Barham;I. Grooms
在线性Eady问题中，我们导出了优化瞬时能量增长率的流动构型的精确解析表达式，以及相关的增长率。这些最优扰动与线性稳定性分析有关，但更重要的是，它们与理解完全非线性斜压湍流的能量学有关。最优摄动及其增长率与理查德森数无关。最优摄动的增长率随着摄动水平波长的减小而线性增长。在大尺度上摄动能量的增长是由从平均气流中提取势能驱动的，而在小尺度上摄动能量的增长是由从平均剪切中提取动能驱动的。我们还分析了空间离散化对最优扰动及其增长率的影响。Arakawa B电网的二阶节能离散化通常在小尺度上的增长率太弱，并且比Arakawa C电网的两个二阶离散化更不准确。两个c网格离散化，一个保存能量，另一个保存能量和熵，产生非常相似的最佳摄动增长率，在小尺度上比b网格离散化要精确得多。
We derive exact analytical expressions for flow configurations that optimize the instantaneous growth rate of energy in the linear Eady problem, along with the associated growth rates. These optimal perturbations are relevant linear stability analysis, but, more importantly, they are relevant for understanding the energetics of fully nonlinear baroclinic turbulence. The optimal perturbations and their growth rates are independent of the Richardson number. The growth rates of the optimal perturbations grow linearly as the horizontal wavelength of the perturbation decreases. Perturbation energy growth at large scales is driven by extraction of potential energy from the mean flow, while at small scales it is driven by extraction of kinetic energy from the mean shear. We also analyze the effect of spatial discretization on the optimal perturbations and their growth rates. A second-order energy-conserving discretization on the Arakawa B grid generally has too weak growth rates at small scales and is less accurate than two second-order discretizations on the Arakawa C grid. The two C-grid discretizations, one that conserves energy and another that conserves both energy and enstrophy, yield very similar optimal perturbation growth rates that are significantly more accurate than the B-grid discretization at small scales.