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首页> 外文期刊>Journal of Physical Oceanography >Instabilities of a Time-Dependent Shear Flow
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Instabilities of a Time-Dependent Shear Flow

机译：时间相关的剪切流的不稳定性

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This study offers a systematic stability analysis of unsteady shear flows representing large-scale, low-frequency internal waves in the ocean. The analysis is based on the unbounded time-dependent Couette model. This setup makes it possible to isolate the instabilities caused by uniform shear from those that can be attributed to resonant triad interactions or to the presence of inflection points in vertical velocity profiles. Linear analysis suggests that time-dependent spatially uniform shears are unstable regardless of the Richardson number (Ri). However, the growth rate of instability monotonically decreases with increasing Ri and increases with increasing frequency of oscillations. Therefore, models assuming a steady basic state-which are commonly used to conceptualize shear-induced instability and mixing-can be viewed as singular limits of the corresponding time-dependent systems. The present investigation is focused on the supercritical range of Richardson numbers (Ri > 1/4) where steady parallel flows are stable. An explicit relation is proposed for the growth rate of shear instability as a function of background parameters. For moderately supercritical Richardson numbers (Ri similar to 1), we find that the growth rates obtained are less than, but comparable to, those expected for Kelvin-Helmholtz instabilities of steady shears at Ri < 1/4. Hence, we conclude that the instability of time-dependent flows could represent a viable mixing mechanism in the ocean, particular in regions characterized by relatively weak wave activity and predominantly supercritical large-scale shears.
机译：这项研究为代表海洋中大规模，低频内波的非恒定剪切流提供了系统的稳定性分析。该分析基于无时限的库埃特模型。这种设置使得可以将均匀剪切所引起的不稳定性与可归因于共振三重轴相互作用或垂直速度曲线中存在拐点的那些相隔离。线性分析表明，与时间相关的空间均匀剪切不稳定，而与理查森数（Ri）无关。但是，不稳定性的增长速率随Ri的增加而单调降低，并随振荡频率的增加而增加。因此，可以将假设为稳态基本状态的模型（通常用于概念化剪切引起的不稳定性和混合）视为相应时间相关系统的奇异极限。目前的研究集中在稳定平行流稳定的理查森数的超临界范围（Ri> 1/4）。提出了与背景参数有关的剪切不稳定性增长率的显式关系。对于中等超临界理查森数（Ri与1相似），我们发现所获得的增长率小于，但与Ri <1/4时稳态剪切的Kelvin-Helmholtz不稳定性所预期的增长率相当。因此，我们得出结论，随时间变化的流动的不稳定性可能代表了海洋中可行的混合机制，特别是在波活动相对较弱且主要是超临界大规模剪切的地区。

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