标题： 单调粘性边界层中的分岔 显示英文标题

标题： Bifurcations in monotonic viscous boundary layers

摘要： 众所周知，当粘度足够小，且水平傅里叶数位于所谓的下边界稳定曲线和上边界稳定曲线之间的某个区间时，剪切层流是线性不稳定的。本文证明了单调剪切层在上边界稳定曲线附近会发生分岔。在指数边界层的特殊情况下，我们证明了这种分岔是霍普夫分岔，这对应于边界附近移动滚动的开始。这种滚动的开始是剪切层流可能“走向混沌”的第一步。 显示英文摘要

摘要： It is well-established that shear layer flows are linearly unstable provided the viscosity is small enough, when the horizontal Fourier number lies in some interval, between the so called lower and upper marginally stable curves. In this article, we prove that monotonic shear layers undergo a bifurcation near the upper marginally stable curve. In the particular case of the exponential boundary layer, we give evidences that this bifurcation is a Hopf bifurcation, which corresponds to the onset of moving rolls near the boundary. The onset of such rolls is the first step of one of the possible ``routes to chaos'' for shear layer flows.