论文标题
瑞利 - 泰勒不稳定的新方法
A new approach to the Rayleigh-Taylor instability
论文作者
论文摘要
在本文中，我们将不均匀的不可压缩的欧拉方程描述了两种在重力影响下具有不同恒定密度不同的流体作为差分包含。通过考虑构成定律的松弛，我们为存在无限的许多弱解的存在制定了一般标准，这些溶液反映了两种流体的湍流混合。在最初流体处于静止状态并被平坦界面隔开的情况下，可以验证我们的标准，而较重的界面在较轻的界面上方 - 经典配置产生了雷利 - 泰勒的不稳定。当Atwood数字在超高范围内时，我们构建了特定的示例，而混合发生的区域随着时间的推移而倍增。
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the constitutive laws we formulate a general criterion for the existence of infinitely many weak solutions which reflect the turbulent mixing of the two fluids. Our criterion can be verified in the case that initially the fluids are at rest and separated by a flat interface with the heavier one being above the lighter one - the classical configuration giving rise to the Rayleigh-Taylor instability. We construct specific examples when the Atwood number is in the ultra high range, for which the zone in which the mixing occurs grows quadratically in time.
