论文标题
在形成粘性腔破裂的卫星形成中的离散自相似性
Discrete self-similarity in the formation of satellites for viscous cavity break-up
论文作者
论文摘要
粘度$μ_{1} $的粘性流体的射流浸入另一种粘度$μ__{2} $的粘液液时，当粘度比$λ=μ___=μ__{1}/μ__{2} $接近零。我们表明，在这个限制下，随着$λ$减少，从普通的连续自相似性转变为离散的自我相似性。结果是，内部射流的破裂不是单点破裂，而是通过出现减小尺寸的细丝的出现，最终会产生外部流体内部流体的气泡的无限序列。该过渡可以理解为在建模物理问题的方程式系统中的HOPF分叉的结果。
The breakup of a jet of a viscous fluid with viscosity $μ_{1}$ immersed into another viscous fluid with viscosity $μ_{2}$ is considered in the limit when the viscosity ratio $λ=μ_{1}/μ_{2}$ is close to zero. We show that, in this limit, a transition from ordinary continuous selfsimilarity to discrete selfsimilarity takes place as $λ$decreases. The result being that instead of a single point breakup, the rupture of the inner jet occurs through the appearance of an infinite sequence of filaments of decreasing size that will eventually produce infinite sequences of bubbles of the inner fluid inside the outer fluid. The transition can be understood as the result of a Hopf bifurcation in the system of equations modelling the physical problem.
