The shear instability of stratified fluids is a well-studied problem in transition to turbulence. In temperate lakes, early springs typically lead to a weak thermal stratification involving water both above and below the temperature at which the density maximum occurs. This implies that mixing of two parcels with the same density, but different temperature, can lead to the creation of denser fluid, a phenomenon known as cabbeling. We report on simulations of shear instability in the cabbeling regime. We find that the initial stages of instability are dominated by shear instability, yielding billows. However, these billows are systematically located below the centerline of the shear layer. Three-dimensionalization occurs through Rayleigh-Taylor-like instabilities, and cabbeling efficiency is greatly increased in the fully three-dimensionalized state. By contrasting with initial states that have the same density profile, but a temperature well outside of the cabbeling regime, we demonstrate that the fully three-dimensional state of the density field is fundamentally different in the cabbeling regime.

中文翻译：

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电缆布线系统中的分层剪切不稳定性

分层流体的剪切不稳定性是向湍流过渡的一个经过充分研究的问题。在温带湖泊中，早春通常会导致较弱的热分层，包括高于和低于出现密度最大值的温度的水。这意味着密度相同但温度不同的两个包裹的混合会导致产生密度更大的流体，这种现象称为 cabbeling。我们报告了缆索系统中剪切不稳定性的模拟。我们发现不稳定的初始阶段主要是剪切不稳定，产生巨浪。然而，这些波浪系统地位于剪切层的中心线下方。三维化通过类似瑞利-泰勒的不稳定性发生，并且在全三维状态下布线效率大大提高。通过与具有相同密度分布但温度远在 cabbeling 范围之外的初始状态进行对比，我们证明了密度场的完全三维状态在 cabbeling 范围内是根本不同的。