Basic two-layer shock-joining theories for internal hydraulic jumps in flows with upstream shear do not have solutions when the shear becomes large. These theories conserve momentum flux and layer-volume-flow-rate across the jump, and conserve energy in either of the two layers to close the set of equations. Alternatively, a closed set of equations conserving vorticity and layer-volume-flow-rate can be used to predict jumps. As shear increases, the physics of the jumps changes, and entrainment becomes important. The theories can be modified to allow entrainment and to indirectly account for continuous velocity profiles, producing solutions where the basic theories failed. These jumps are investigated to illuminate the changing physics as shear increases. Simulations show that the amount of entrainment is related to the square of the upstream shear in both 2D and 3D simulations. However, they also show that the two-layer approximation becomes increasingly inaccurate, and 2D and 3D simulations disagree, at very high shear values. Furthermore, super- to super-critical transitions are also possible at higher shear, and while they exhibit a more gradual transition than a hydraulic jump, they can be analyzed using the same framework. The simulation results also illustrate the changing structure, vorticity balance, mixing, and energetic properties of the jumps as the upstream shear increases.

中文翻译：

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随着上游剪切力的增加，两层流中的内部液压跃变

当剪切力变大时，在上游剪切力作用下内部水力跃迁的基本两层减震理论没有解决方案。这些理论保存跨跃点的动量通量和层体积流率，并保存两层中任一层的能量以关闭方程组。可替代地，可以将守恒涡度和层体积流量的一组封闭方程组用于预测跳跃。随着剪切力的增加，跳跃的物理性质发生变化，并且夹带变得重要。可以修改这些理论以允许夹带并间接考虑连续速度分布，从而在基本理论失败的情况下产生解决方案。对这些跃变进行了研究，以阐明随着剪切力增加而变化的物理现象。仿真表明，在2D和3D仿真中，夹带量与上游剪切力的平方有关。但是，他们还表明，在非常高的剪切值下，两层逼近变得越来越不准确，并且2D和3D模拟也不相同。此外，在较高的剪切力下，超临界至超临界的过渡也是可能的，尽管它们显示出比水力跃变更平缓的过渡，但可以使用相同的框架进行分析。仿真结果还说明了随着上游剪切力的增加，跳跃的结构，涡旋平衡，混合和能量特性发生变化。在较高的剪切力下，超临界至超临界的过渡也是可能的，尽管它们显示出比液压跃变更平缓的过渡，但可以使用相同的框架进行分析。仿真结果还说明了随着上游剪切力的增加，跳跃的结构，涡旋平衡，混合和能量特性发生变化。在较高的剪切力下，超临界至超临界的过渡也是可能的，尽管它们显示出比液压跃变更平缓的过渡，但可以使用相同的框架进行分析。仿真结果还说明了随着上游剪切力的增加，跳跃的结构，涡旋平衡，混合和能量特性发生变化。