论文标题
放松BousSinesQ系统和雷利 - 泰勒不稳定性的应用
Relaxation of the Boussinesq system and applications to the Rayleigh-Taylor instability
论文作者
论文摘要
我们考虑两种具有均匀密度的不可压缩流体的演变，$ρ_- <ρ_+$由Inviscid Boussinesq方程描述的重力，并提供了相关差分包含的明确放松。放松的订阅的存在使人们可以得出结论将溶液混合到原始的Boussinesq系统中的存在。作为特定应用，我们研究了从经典的雷利 - 泰勒初始配置产生的种植，其中两种流体通过水平界面分离，较重的流体在较轻的顶部。事实证明，在所有自相似的亚物物中，最大初始能量耗散的标准选择了线性密度曲线和混合区的二次生长。选择以这种方式选择的订阅可以以可接受的方式扩展。我们提供两个可能的长期限制的可能扩展。第一个对应于两种流体的总混合物，第二个对应于完全分离的，而较轻的液体在较重的顶部。任何极限状态都没有运动。
We consider the evolution of two incompressible fluids with homogeneous densities $ρ_-<ρ_+$ subject to gravity described by the inviscid Boussinesq equations and provide the explicit relaxation of the associated differential inclusion. The existence of a subsolution to the relaxation allows one to conclude the existence of turbulently mixing solutions to the original Boussinesq system. As a specific application we investigate subsolutions emanating from the classical Rayleigh-Taylor initial configuration where the two fluids are separated by a horizontal interface with the heavier fluid being on top of the lighter. It turns out that among all self-similar subsolutions the criterion of maximal initial energy dissipation selects a linear density profile and a quadratic growth of the mixing zone. The subsolution selected this way can be extended in an admissible way to exist for all times. We provide two possible extensions with different long-time limits. The first one corresponds to a total mixture of the two fluids, the second corresponds to a full separation with the lighter fluid on top of the heavier. There is no motion in either of the limit states.
