We formulate an expression for the turbulent kinetic energy dissipation rate, ϵ, associated with shear‐generated turbulence in terms of quantities in the ocean or atmosphere that, depending on the situation, may be measurable or resolved in models. The expression depends on the turbulent vertical length scale, ℓ_v, the inverse time scale N, and the Richardson number Ri = N²/S², where S is the vertical shear, with ℓ_v scaled in a way consistent with theories and observations of stratified turbulence. Unlike previous studies, the focus is not so much on the functional form of Ri, but the vertical variation of the length scale ℓ_v. Using data from two ∼7‐day time series in the western equatorial Pacific, the scaling is compared with the observed ϵ. The scaling works well with the estimated ϵ capturing the differences in amplitude and vertical distribution of the observed ϵ between the two times series. Much of those differences are attributable to changes in the vertical distribution of the length scale ℓ_v, and in particular the associated turbulent velocity scale, u_t. We relate u_t to a measure of the fine‐scale variations in velocity, . Our study highlights the need to consider the length scale and its estimation in environmental flows. The implications for the vertical variation of the associated turbulent diffusivity are discussed.

中文翻译：

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剪切产生湍流的尺度：赤道温跃层，一个案例研究

我们制定湍流动能耗散率，表达ε，带有剪切紊流产生在海洋或大气的是，根据不同的情况，可能是可测量或模型解决数量方面有关。的表达依赖于湍流垂直长度尺度，ℓ _v，逆时间标度Ñ，和Richardson数日 =  Ñ ² / s ^ ²，其中小号是垂直剪切，与ℓ _v与理论和观察结果是一致的方式按比例分层湍流。与之前的研究不同，本文的重点不是功能的形式里，但长度尺度的垂直变化ℓ _v。利用来自赤道西太平洋的两个〜7天时间序列的数据，将尺度与观测到的ϵ进行比较。缩放与所估计的工作良好ε捕获在幅度和所观察到的的垂直分布的差异ε两个时间系列之间。多的这些差异是由于在长度尺度的垂直分布的变化ℓ _v，特别是相关的湍流速度标尺，Ú _Ť。我们与ü_牛逼的精细尺度变化的措施的速度，。我们的研究强调需要考虑长度尺度及其在环境流量中的估计。讨论了相关湍流扩散率在垂直方向上的变化。