The evolution of Tollmien–Sclichting waves near a leading edge
The evolution of Tollmien–Sclichting waves near a leading edge
复制标题
DOI：
10.1017/s002211208300261x
复制
发表时间：
1983-02
影响因子：
3.7
通讯作者：
By M. E. Goldstein
中科院分区：
文献类型：
--
作者：
By M. E. Goldstein
本文用匹配渐近展开法研究了自由流扰动入射平板边界层时Tollmien-Schlichting波的产生。在前缘附近，运动由非定常边界层方程控制，而在更远的下游，则由具有缓慢变化系数的Orr-Sommerfeld方程控制（到最低阶）。它表明，有一个重叠域的Tollmien-Schlichting波解决方案的Orr-Sommerfeld方程和适当的渐近解的非定常边界层方程匹配，在匹配的渐近展开的意义。该分析解释了长波长自由流扰动如何产生波长短得多的Tollmien-Schlichting波。它还导致了一组的非定常边界层的渐近结构的标度律。
The method of matched asymptotic expansions is used to study the generation of Tollmien-Schlichting waves by free-stream disturbances incident on a flat-plate boundary layer. Near the leading edge, the motion is governed by the unsteady boundary-layer equation, while farther downstream it is governed (to lowest order) by the Orr-Sommerfeld equation with slowly varying coefficients. It is shown that there is an overlap domain where the Tollmien-Schlichting wave solutions to the Orr-Sommerfeld equation and appropriate asymptotic solutions of the unsteady boundary-layer equation match, in the matched-asymptotic-expansion sense. The analysis explains how long-wavelength free-stream disturbances can generate Tollmien-Schlichting waves of much shorter wavelength. It also leads to a set of scaling laws for the asymptotic structure of the unsteady boundary layer.