Applied Mathematics and Mechanics

, Volume 29, Issue 1, pp 1–8 | Cite as

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

  • Zhang Yong-ming  (张永明)
  • Zhou Heng  (周恒)Email author


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.

Key words

parabolized stability equations secondary instability fundamental disturbances sub-harmonic waves 

Chinese Library Classification


2000 Mathematics Subject Classification



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Copyright information

© Editorial Committee of Appl. Math. Mech. and Springer-Verlag 2008

Authors and Affiliations

  • Zhang Yong-ming  (张永明)
    • 1
  • Zhou Heng  (周恒)
    • 1
    • 2
    Email author
  1. 1.Department of MechanicsTianjin UniversityTianjinP. R. China
  2. 2.LIU Hui Center of Applied Mathematics of Nankai University and Tianjin UniversityTianjinP. R. China

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