非地转Eady模式中的瞬时能量增长
Transient energy growth in the ageostrophic Eady model
摘要：
本文重新讨论了热成风切变中的最佳初始扰动问题，并将其扩展到包括非静力效应。这项系统的研究比较了瞬态和模态增长率的次中尺度不稳定性在很大范围内的纬向和纬向波数，长宽比，和不同的理查森数制度。导出了选择准则以去除由本征值问题引起的虚假和未解决的不稳定模式，并且我们将Heifetz和Farrell（2003，2007，2008）对流体静力Eady问题的研究推广到以大展弦比为特征的薄锋。这种锋面通常出现在锋生的早期阶段，例如，在海洋中尺度涡旋和飓风眼壁附近。特别是，我们表明，瞬态能量的增长率是两个数量级以上的模态对应的Richardson数的范围很广，瞬态能量增益的影响变得更大时，非流体静力学效应变得重要和/或大Richardson数。本研究还比较了在短期和长期的能量增长的主要能源途径。对于对称模式，我们恢复了徐等人（2007）中描述的惯性-重力不稳定性。与增长最快的斜压和对称模式相比，这些机制被证明是最强大的介质的垂直输送。这些结果突出了海洋和大气中瞬变过程的重要性。
英文摘要：
The problem of optimal initial disturbances in thermal wind shear is revisited and extended to include non-hydrostatic effects. This systematic study compares transient and modal growth rates of submesoscale instabilities over a large range of zonal and meridional wave numbers, aspect ratios, and different Richardson number regimes. Selection criteria were derived to remove spurious and unresolved instability modes that arise from the eigenvalue problem and we generalize the study of the hydrostatic Eady problem by Heifetz and Farrell (2003, 2007, 2008) to thin fronts, characterized by large aspect ratios. Such fronts are commonly found at the early stages of frontogenesis, for example, in the ocean mesoscale eddies and near the eye wall of hurricanes. In particular, we show that transient energy growth rates are up to two orders of magnitude larger than modal counterparts for a wide range of Richardson number and that the effects of transient energy gain become even greater when non-hydrostatic effects become important and/or for large Richardson numbers. This study also compares the dominant energy pathways contributing to the energy growth at short and long times. For symmetric modes, we recover the inertia-gravity instability described in Xu et al. (2007). These mechanisms are shown to be the most powerful mediator of vertical transport when compared with the fastest growing baroclinic and symmetric modes. These results highlight the importance of transient processes in the ocean and the atmosphere.
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