PSE as applied to problems of secondary instability in supérsonic boundary layers  

作　　者：张永明 周恒 

机构地区：[1]Department of Mechanics,Tianjin University [2]Department of Mechanics,Tienjin University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2008年第1期1-8,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.10632050,90716007);the Foundation of LIU Hui Center of Applied Mathematics of Nankai University and Tianjin University

摘　　要：Parabolized stability equations （PSE） approach is used to investigate problems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether the 2-D fundamental disturbance is of the first mode or second mode T-S wave. The variation of the growth rates of the 3-D sub-harmonic wave against its span-wise wave number and the amplitude of the 2-D fundamental wave is found to be similar to those found in incompressible boundary layers. But even as the amplitude of the 2-D wave is as large as the order 2%, the maximum growth rate of the 3-D sub-harmonic is still much smaller than the growth rate of the most unstable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.Parabolized stability equations （PSE） approach is used to investigate problems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether the 2-D fundamental disturbance is of the first mode or second mode T-S wave. The variation of the growth rates of the 3-D sub-harmonic wave against its span-wise wave number and the amplitude of the 2-D fundamental wave is found to be similar to those found in incompressible boundary layers. But even as the amplitude of the 2-D wave is as large as the order 2%, the maximum growth rate of the 3-D sub-harmonic is still much smaller than the growth rate of the most unstable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.

关 键 词：parabolized stability equations secondary instability fundamental disturbances sub-harmonic waves 

分 类 号：O357.41[理学—流体力学]