Mathematical Sciences: Stability and Bifurcation in Two-Layer Flows

[902166] Renardy：本文将研究两种非混相流体的两层流的稳定性和分岔问题。这种流动在工业上有许多应用，如双组分纤维的形成、管道中石油的输送、喷墨印刷和润滑。众所周知，根据我们对单流体流动的了解，这种流动也会表现出完全意想不到的现象。理论上，两种流体的边界形状存在多种可能性。然而，实验表明，一些形状比其他形状更受青睐，尽管潜在的选择机制尚未得到很好的理解。本文的主要目的是用分析和计算的方法研究两层流动的各种稳定排列的稳定性，以及从不稳定排列演变成新的排列。

8902166 Renardy This proposal will study the stability and bifurcation in two-layer flows involving two immiscible fluids. Such flows have many applications in industry, such as the formation of bicomponent fibers, the transport of oil in pipelines, ink-jet printing and lubrication. It is well known that such flows can also exhibit phenomena which are totally unexpected based on our knowledge of one-fluid flows. Theoretically, many possibilities exist for the shape of the boundary separating the two fluids. Yet experiments show that some shapes are preferred over others, although the underlying selection mechanisms are not well understood. A chief objective of this proposal is to study, analytically and computationally, the stability of the various steady arrangements of two-layer flows, and the evolution of new arrangements from unstable ones.