Mathematical Sciences: Solitons and the Onset of Chaotic Pulsation in Boundary Layers

9404315将在渐近三层理论的框架内考虑层流边界层中基本非线性稳定性的Cole方面。自由气流中的扰动，如涡度或声音，导致波包经历爆炸性增长。非线性扰动用一个受迫的Benjamin-Ono方程描述。在过渡的过程中，预计会出现混乱的脉动。本文的结果主要应用于边界层流动的层流-湍流转变的预测，例如飞机或喷气发动机上的流动。对湍流的理解和控制将使更有效的设计成为可能。在出现大的非线性波动系统的大气中也观察到了类似的扰动。这里的理论工作可以更好地理解地形和风暴的相互作用。

9404315 Cole Aspects of essentially nonlinear stability in the laminar boundary layer will be considered in the framework of the asymptotic triple deck theory. Disturbances in the free stream such as vorticity or sound result in wave packets which undergo explosive growth. The nonlinear disturbances are described by a forced Benjamin-Ono equation. Chaotic pulsations are expected to result on the way to transition. The results here have their primary application to the prediction of laminar-turbulent transition in boundary layer flows, such as those on aircraft or in jet engines. The understanding and control of turbulence will make more efficient designs possible. Similar disturbances have been observed in the atmosphere where large nonlinear wave systems appear. The theoretical work here can lead to a better understanding of the interaction of topography and storms.