We perform the stability analysis for a free surface fluid current modeled as two finite layers of constant vorticity, under the action of gravity and absence of surface tension. In the same spirit as Taylor ["Effect of variation in density on the stability of superposed streams of fluid," Proc. R. Soc. A 132, 499 (1931)], a geometrical approach to the problem is proposed, which allows us to present simple analytical criteria under which the flow is stable. A strong destabilizing effect of stratification in density is revealed by comparison with the physical setting where the vorticity interface is also a density interface separating two immiscible fluids with constant densities.

中文翻译：

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密度变化对自由表面双线性剪切流稳定性的影响

我们对自由表面流体流进行稳定性分析，该流被建模为两个有限的恒定涡量层，在重力和没有表面张力的作用下。本着与泰勒相同的精神 [“密度变化对叠加流体流稳定性的影响”，Proc。R. Soc。A 132, 499 (1931)]，提出了解决该问题的几何方法，它允许我们提出简单的分析标准，在该标准下流动是稳定的。通过与涡度界面也是分隔具有恒定密度的两种不混溶流体的密度界面的物理设置进行比较，揭示了密度分层的强烈不稳定效应。