Stability of a Flow Over Bottom Topography: A General Condition and a Linear Analysis in a Two‐Layer Quasi‐Geostrophic Model With a Possible Application to a Kuroshio Meander
Stability of a Flow Over Bottom Topography: A General Condition and a Linear Analysis in a Two‐Layer Quasi‐Geostrophic Model With a Possible Application to a Kuroshio Meander
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底部地形流的稳定性：双层准地转模型中的一般条件和线性分析以及可能应用于黑潮曲流的情况
DOI：
10.1029/2021jc017849
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Tanaka Yuki
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文献类型：
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作者：
野口高明;松本理佳子;薮田ひかる;小林華栄;三宅亮;奈良岡浩;岡崎隆司;今栄直也;山口亮;キルコイン・デービッド;武市康男;高橋嘉夫;Yasutaka Hirockawa and Teruyuki Kato;Tanaka Yuki
本文用一种获得稳定性充分条件的方法和一种线性稳定性分析相结合的方法研究了海底地形上两层准地转流的稳定性。首先，利用与扰动振幅平方成正比的赝能守恒量，导出了位涡与流函数成正比的最简单定常背景场稳定性的充分条件。理论上得到的条件使我们能够判断各种背景场的稳定性，明确考虑到域的大小和/或边界条件的扰动的规模上施加的限制。将稳定性条件应用到正弦背景流和地形的特殊情况下，则表明稳定范围延伸到在上层和下层的右侧水流较浅的区域。当扰动局限于较小的水平尺度时，稳定范围变宽。线性稳定度分析表明，这种展宽主要是由于正压不稳定的抑制，有效地在大尺度工作。最后，数值模拟进行了一个现实的情况下，黑潮弯曲在日本南部的海山铭记。结果表明，该理论是有用的，以确定一个稳定的流与负定的伪能量，这可以实现在现实的海洋条件下，扰动的规模是适度限制由突出的地形特征所界定的盆地。
The stability of a two‐layer quasi‐geostrophic flow over bottom topography is examined by combining a method of obtaining a sufficient condition for stability and a linear stability analysis. First, using a conserved quantity called pseudoenergy that is proportional to the square of the disturbance amplitude, a sufficient condition for stability is derived for the simplest steady background field in which the potential vorticity and the stream function are proportional to each other. The theoretically obtained condition enables us to judge the stability of various background fields by explicitly taking into account the limitation imposed on the scale of the disturbance by the domain size and/or boundary conditions. Applying the stability condition to a special case of a sinusoidal background flow and topography then shows that the stable range extends to the area where the currents flow with shallower water on their right in both the upper and lower layers. The stable range is broadened as the disturbance becomes limited to smaller horizontal scales. A linear stability analysis shows that this broadening is mainly due to the suppression of barotropic instability that works effectively at large scales. Finally, a numerical simulation is performed with a realistic situation of a Kuroshio meander over a seamount south of Japan in mind. The results suggest that the theory is useful to identify a stable flow with negative‐definite pseudoenergy, which can be achieved under realistic ocean conditions where the scale of the disturbance is moderately restricted by a basin bounded by prominent topographic features.