The Rayleigh–Taylor instability for inviscid and viscous fluids
The Rayleigh–Taylor instability for inviscid and viscous fluids
复制标题
无粘性和粘性流体的瑞利-泰勒不稳定性
DOI：
10.1007/s10665-009-9288-9
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发表时间：
2009
影响因子：
1.3
通讯作者：
L. Forbes
中科院分区：
文献类型：
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作者：
L. Forbes
经典的瑞利-泰勒不稳定性发生在两种无黏性流体，有一个尖锐的界面将它们分开，处于两个水平层中，较重的流体在较轻的流体之上。在这种不稳定的情况下，当较重的上部流体开始向下穿过较轻的下部流体时，界面上的小正弦扰动会迅速增长。本文提出了一种新的计算界面生长的数值方法。该技术基于溶液的谱表示。结果是准确的，直到界面处曲率奇点形成，无粘模型失效。然后提出了一种谱方法来研究粘性布辛涅斯克流体的不稳定性。结果表明，在小到中等时间内，计算结果与无粘计算结果非常吻合。然而，在无粘模型中产生的高界面曲率在粘性流体中不会发生，因为正是在这些奇异点处出现了高涡度区域。这导致界面翻转，形成蘑菇形状的轮廓。结果表明，不同的初始界面构型会导致非常不同的几何结果，这是流动不稳定性的结果。这些可能包括在流体中形成分离气泡的情况。
The classical Rayleigh–Taylor instability occurs when two inviscid fluids, with a sharp interface separating them, lie in two horizontal layers with the heavier fluid above the lighter one. A small sinusoidal disturbance on the interface grows rapidly in time in this unstable situation, as the heavier upper fluid begins to move downwards through the lighter lower fluid. This paper presents a novel numerical method for computing the growth of the interface. The technique is based on a spectral representation of the solution. The results are accurate right up to the time when a curvature singularity forms at the interface and the inviscid model loses its validity. A spectral method is then presented to study the same instability in a viscous Boussinesq fluid. The results are shown to agree closely with the inviscid calculations for small to moderate times. However, the high interface curvatures that develop in the inviscid model are prevented from occurring in viscous fluid by the growth of regions of high vorticity at precisely these singular points. This leads to over-turning of the interface, to form mushroom-shaped profiles. It is shown that different initial interface configurations can lead to very different geometrical outcomes, as a result of the flow instability. These can include situations when detached bubbles form in the fluid.