On Baroclinic Instability over Continental Shelves: Testing the Utility of Eady-Type Models
On Baroclinic Instability over Continental Shelves: Testing the Utility of Eady-Type Models
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DOI：
10.1175/jpo-d-19-0175.1
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发表时间：
2020-01
影响因子：
3.5
通讯作者：
Shih-Nan Chen;Chiou-Jiu Chen;J. Lerczak
中科院分区：
文献类型：
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作者：
Shih-Nan Chen;Chiou-Jiu Chen;J. Lerczak
本研究探讨了 Eady 型理论在理解沿海流中斜压不稳定性的实用性，其中深度变化和底部阻力很重要。重点是非地转、边界耗散和底部坡度的影响。该方法将理论推导的不稳定性特性与数值模型计算进行比较，用于旨在隔离个体影响并证明具有类似 Eady 的基本状态的实验。对于非地转效应，Stone（1966）的理论被证明可以对最不稳定的生长速率和波长给出合理的预测。研究还表明，完全非线性模型中不断增长的不稳定性可以解释为边界捕获罗斯贝波相互作用，即波锁相和向西相位倾斜允许波相互放大。分析表明，边界耗散效应和底部坡度效应都可以通过不稳定内部下边界处的垂直速度来表示，分别通过诱导 Ekman 泵浦和坡度平行流，如 Williams 和 Robinson（1974；称为 Eady-Ekman 问题）以及 Blumsack 和 Gierasch（1972）的理论所提出的。以摩擦参数和坡度比为特征的垂直速度修改底部波，从而修改尺度选择。然而，这些理论具有固有的定量局限性。 Eady-Ekman 忽略了限制底部应力增加的边界层响应，从而高估了大阻力下的 Ekman 泵送和增长率降低。 Blumsack 和 Gierasch（1972）的模型忽略了平均流中斜坡引起的水平剪切，该剪切使涡流倾斜以有利于将能量转换回平均值，因此在陡坡上的实用性有限。
This study examines the utility of Eady-type theories as applied to understanding baroclinic instability in coastal flows where depth variations and bottom drag are important. The focus is on the effects of nongeostrophy, boundary dissipation, and bottom slope. The approach compares theoretically derived instability properties against numerical model calculations, for experiments designed to isolate the individual effects and justified to have Eady-like basic states. For the nongeostrophic effect, the theory of Stone (1966) is shown to give reasonable predictions for the most unstable growth rate and wavelength. It is also shown that the growing instability in a fully nonlinear model can be interpreted as boundary-trapped Rossby wave interactions—that is, wave phase locking and westward phase tilt allow waves to be mutually amplified. The analyses demonstrate that both the boundary dissipative and bottom slope effects can be represented by vertical velocities at the lower boundary of the unstable interior, via inducing Ekman pumping and slope-parallel flow, respectively, as proposed by the theories of Williams and Robinson (1974; referred to as the Eady–Ekman problem) and Blumsack and Gierasch (1972). The vertical velocities, characterized by a friction parameter and a slope ratio, modify the bottom wave and thus the scale selection. However, the theories have inherent quantitative limitations. Eady–Ekman neglects boundary layer responses that limit the increase of bottom stress, thereby overestimating the Ekman pumping and growth rate reduction at large drag. Blumsack and Gierasch’s (1972) model ignores slope-induced horizontal shear in the mean flow that tilts the eddies to favor converting energy back to the mean, thus having limited utility over steep slopes.