论文标题
临界密度三胞胎，用于捕获落入急剧分层的液体中的球体
Critical density triplets for the arrestment of a sphere falling in a sharply stratified fluid
论文作者
论文摘要
我们研究了潜在的流动状态下重力作用下的刚性球的运动。在大约20至450的中等雷诺数的实验表明，具有精确临界密度（高于底层密度）的球体可以显示越过界面后的弹跳或逮捕行为。我们在实验上证明，随着底流体密度随着固定顶流体密度的增加，这种临界球密度随着底部流体密度的增加而线性增加。此外，随着密度过渡层的厚度增加，临界密度接近底层流体密度。我们提出了基于势能的临界密度估计。在假设零层厚度的情况下，估计构成了临界密度的上限，在实验密度状态下，在零层厚度假设下，实验密度状态在0.997 $ g/cm^{3} $ $ $ $ $ $ $ $ \ sim $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $ 1.11 $^{3} $中。通过与实验层厚度匹配，我们获得了一个临界密度估计，在同一参数状态下，相对差异小于0.01。
We study the motion of a rigid sphere falling in a two-layer stratified fluid under the action of gravity in the potential flow regime. Experiments at a moderate Reynolds number of approximately 20 to 450 indicate that a sphere with the precise critical density, higher than the bottom layer density, can display behaviors such as bounce or arrestment after crossing the interface. We experimentally demonstrate that such a critical sphere density increases linearly as the bottom fluid density increases with a fixed top fluid density. Additionally, the critical density approaches the bottom layer fluid density as the thickness of density transition layer increases. We propose an estimation of the critical density based on the potential energy. With assuming the zero layer thickness, the estimation constitutes an upper bound of the critical density with less than 0.043 relative difference within the experimental density regime 0.997 $g/cm^{3}$ $\sim $ 1.11 $g/cm^{3}$ under the zero layer thickness assumption. By matching the experimental layer thickness, we obtain a critical density estimation with less than 0.01 relative difference within the same parameter regime.
