球体在急剧分层流体中下落时的临界密度三重态
Critical density triplets for the arrestment of a sphere falling in a sharply stratified fluid
摘要：
本文研究了势流区中，在重力作用下，刚性球体在两层分层流体中的下落运动。在大约20到450的中等雷诺数下的实验表明，具有精确的临界密度（高于底层密度）的球体在穿过界面后可以显示诸如反弹或收缩的行为。我们的实验表明，这样的临界球密度线性增加的底部流体密度的增加与固定的顶部流体密度。随着密度过渡层厚度的增加，临界密度逐渐接近底层流体密度。我们提出了一个估计的临界密度的基础上的势能。假设层厚度为零，该估计构成了临界密度的上限，在零层厚度假设下，实验密度范围为0.997 $g/cm^{3}$ $\sim $ 1.11 $g/cm^{3}$，相对差小于0.043。通过匹配实验层厚度，我们得到了一个临界密度估计小于0.01的相对差异内相同的参数制度。
英文摘要：
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.
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