Acta Mechanica Sinica

, Volume 19, Issue 6, pp 517–526 | Cite as

Studies on nonlinear stability of three-dimensional H-type disturbance

  • Wang Weizhi
  • Tang Dengbin


The three-dimensional H-type nonlinear evolution process for the problem of boundary layer stability is studied by using a newly developed method called parabolic stability equations (PSE). The key initial conditions for sub-harmonic distrubances are obtained by means of the secondary instability theory. The initial solutions of two-dimensional harmonic waves are expressed in Landau expansions. The numerical techniques developed in this paper, including the higher order spectrum method and the more effective algebraic mapping for dealing with the problem of an infinite region, increase the numerical accuracy and the rate of convergence greatly. With the predictor-corrector approach in the marching procedure, the normalization, which is very important for PSE method, is satisfied and the stability of the numerical calculation can be assured. The effects of different pressure gradients, including the favorable and adverse pressure gradients of the basic flow, on the “H-type” evolution are studied in detail. The results of the three-dimensional nonlinear “H-type” evolution are given accurately and show good agreement with the data of the experiment and the results of the DNS from the curves of the amplitude variation, disturbance velocity profile and the evolution of velocity.

Key Words

three-dimensional disturbance H-type nonlinear stability boundary layer parabolic stability equations 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Malik MR, Balakumar P. Linear stability of three-dimensional boundary layers: effects of curvature and non-parallelism. AIAA Paper, 93-0079, 1993Google Scholar
  2. 2.
    Saric WC, Kozlor VV, Levchenko VY. Forced and unforced subharmonic resonance in boundary layer transition. AIAA, 22nd Aerospace Science Meeting January 1984/Reno, Nevada, 9–12Google Scholar
  3. 3.
    Herbert T, Bertolotti FP. Stability analysis of nonparallel boundary layer.J Bull Am Phys Soc, 1987, 32: 2079–2806Google Scholar
  4. 4.
    Herbert T. On the stability of 3d boundary layers. AIAA Paper 97-1961, 1997Google Scholar
  5. 5.
    Bertolotti FP. Linear and nonlinear stability of boundary layers with streamwise varying properties: [Ph D Thesis]. The Ohio State University, 1991. 148–151Google Scholar
  6. 6.
    Zhao GF, Meng QG, Wang DY. On secondary instability in Blasius boundary layer flow.Mechanics and Practice, 1992, 14(4): 25–29Google Scholar
  7. 7.
    Zhao GF. Secondary instability with respect to spatial growing three-dimensional subharmonic disturbance in boundary layer flow with suction.Journal of Hydrodynamics, Ser B, 1995, 3: 7–12MATHGoogle Scholar
  8. 8.
    Wang WZ, Tang DB. On secondary instability with respect to spatial evolution in Falkner Skan flow.Acta Aerodynamica Sinica, 2002, 20(4): 477–482Google Scholar
  9. 9.
    Orszag ST. Accurate solution of the Orr-Sommerfeld stability equation.J Fluid Mech, 1971, 50: 689–703MATHCrossRefGoogle Scholar
  10. 10.
    Grosch CE, Orszag SA. Numerical solution of problems in unbounded regions: coordinate transforms.Journal of Computational Physics, 1977, 25: 273–296MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Kachanov YS, Levchenko VY. The resonant of disturbance at laminar-turbulent transition in boundary layer.J Fluid Mech, 1984, 138: 209–247CrossRefGoogle Scholar
  12. 12.
    Fasel HF, Rist U, Konzelmann U. Numerical investigation of the three-dimensional development in a boundary layer transition.AIAA J, 1990, 28: 29–37MathSciNetCrossRefGoogle Scholar

Copyright information

© Chinese Society of Theoretical and Applied Mechanics 2003

Authors and Affiliations

  • Wang Weizhi
    • 1
  • Tang Dengbin
    • 1
  1. 1.Department of AerodynamicsNanjing University of Aeronautics and AstronauticsNanjingChina

Personalised recommendations